Israel Gaza live updates: IDF says it controls Gaza side of Rafah ...

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Conflict has continued a day after Hamas accepted truce terms offered by Qatari and Egyptian mediators, which Israel rejected as being far from its "basic requirements". Here's the latest:

Stay with us and we'll continue to bring you live updates, and you can watch live coverage on our BBC News Channel stream by clicking play at the top of this page.

We've just been getting the latest on the BBC News channel from our reporters in Cairo and Jerusalem.

Jo Floto, our Middle East Bureau Chief in Jerusalem, says Israel's special forces are currently combing Rafah in search of what they call "terrorist infrastructure".

Israel has already announced that it has found three tunnels, and these tunnels are key to why the IDF wants to be in this area of Gaza, Floto says. Israel has long suspected that this is the entry point for weaponry and other supplies to militant groups like Hamas, he adds.

In Cairo, BBC Arabic reporter Abdelbassir Hassan says no officials will confirm whether delegations from Israel or Hamas have arrived for ceasefire negotiations.

He says that Egypt, a mediator in these negotiations, is showing restraint in its reaction to the development that Israel is now operating right up against its border between the Gaza Strip. Egypt has condemned Israel's control of the Rafah crossing, as has Qatar, another mediator in these talks. Neither want any enlargement of this conflict.

We've been covering the ongoing ceasefire talks in our last few posts so let's switch gears and look at the situation on the ground Gaza.

People are continuing to leave Rafah after Israel ordered about 100,000 civilians to evacuate parts of the southern city, which has been a refuge for displaced Palestinians.

Here are the latest photos of people on the move:

Hamas's acceptance of (undisclosed) proposals appeared to offer a moment of hope in a months-long cycle of progress and setbacks.

Momentum which led to Monday's statement by Hamas was kick-started just over a week ago, when an official from the group said it had "no major issues" with the latest proposal.

At the same time, US Secretary of State Antony Blinken said the US was “hopeful” Hamas would accept the proposal, which he called “extraordinarily generous”.

The terms were not publicised, but reports suggested that Israel had found a new form of words about a pause in fighting – talking about a "sustainable calm" in Gaza – something between a truce and a ceasefire.

A day later, Israeli Prime Minister Benjamin Netanyahu said an offensive against Hamas in Rafah would go ahead regardless of whether there was a truce - raising doubts over Hamas's willingness to give a positive answer.

Hopes were further dimmed on Sunday when talks in Cairo between Hamas and mediators stalled, with Israel and Hamas blaming each other.

A rocket attack from Rafah by Hamas the same day which killed four Israeli soldiers, swiftly followed by Israeli air strikes on Rafah which reportedly killed 19 Palestinians - and Israel's order hours later for Palestinians to evacuate parts of Rafah - deepened a growing sense of pessimism.

So when Hamas's leadership issued its statement on Monday evening saying they had approved the Egyptian and Qatari-mediated proposal, it bucked expectations.

Neither Israel nor Hamas want to be held responsible for failing to reach a ceasefire - so each is showing they're prepared to keep going, as the urgency grows by the day.

A group of "mid-ranking" Israeli envoys will go to Cairo in the next few hours to see if Hamas can be persuaded to change its latest ceasefire offer, a senior Israeli official tells Reuters news agency.

The official reiterates that the current proposal is unacceptable, adding: "This delegation is made up of mid-level envoys. Were there a credible deal in the offing, the principals would be heading the delegation."

Hamas said yesterday that it would accept a deal drawn up by Egyptian mediators, but it's not clear what exactly is in the deal Hamas has agreed to and Israel rejected the proposal, saying it was "far from meeting" its "core demands".

Dennis Ross, a former US Middle East envoy, tells BBC Radio 4's Today programme that Israeli Prime Minister Benjamin Netanyahu is in a "difficult position" when it comes to agreeing any potential ceasefire deal.

Israel's Finance Minister Bezalel Smotrich and National Security Minister Itamar Ben-Gvir have both said they would quit the government over the terms Israel was prepared to put on the table, Ross says, adding it is an "open question" as to whether they are bluffing.

But if the terms Hamas says it will accept are close to what Netanyahu has already agreed to present, Ross says it "won't be so easy for him to turn it down", adding that if Netanyahu was to do so, there is a "high risk" that other figures in the government could leave.

"That doesn't bring the government down the way Smotrich and Ben-Gvir would, but it may set in motion a set of events in Israel that I think could put the government at risk," he says.

"At a certain point, he needs to choose Biden over Ben-Gvir, he needs to choose the hostages over Smotrich".

A former Israeli MP for Benjamin Netanyahu's Likud party says he believes if Hamas is serious about accepting a deal which would see all hostages returned to Israel, then Israel would sign the deal too.

Michael Kleiner, who's now president of the Likud party's internal court, tells BBC Radio 4's Today programme that Israel can't declare victory in its military action against Hamas until all of the hostages are home.

But at the moment, Israeli officials will be examining how "serious" Hamas is in accepting the proposal for a new Gaza ceasefire and hostage release deal with Israel, he says.

Meanwhile in Rafah, Kleiner adds, "the pace of the activity... will not be accelerated, just preparation action, not full scale war".

"If (Hamas leader) Sinwar is serious, there will be a deal," he says.

Sharone Lifschitz, whose 83-year-old father Oded is still missing, presumed to be held captive in the Gaza Strip, says she's not hopeful about truce talks continuing because "there are extremists on both sides that can derail it".

Speaking to BBC 4's Today programme, she says she hopes Israel's government will follow what the majority of Israeli citizens want and "bring this deal so that our loved ones could come back".

Sharone's mother was freed from Hamas captivity in Gaza in October but she says her family hasn't had proof of life for her father since the 20th day of his captivity.

"If my father is alive it is a miracle, we can’t wait to have him back, we can’t wait to hug him," says Lifschitz.

Quote Message: If it doesn’t happen now it is going to take very long. We know some of them are dead, we know that they are in harm's way every day and every hour. We need to find a way to negotiate long term deals to provide the security of citizens of Israel and Palestine. I urge the government to do all it can to bring back our people."

James Landale

Diplomatic correspondent

In diplomatic terms, the most interesting question now is what the Americans say and do.

Because overnight their briefers have been very, very cautious, refusing to say anything substantive about the Hamas announcement, simply saying that a deal is achievable and that they oppose, and they continue to oppose, any military operation in Rafah.

But on the substance they have remained remarkably quiet.

And that is because if the Americans at any stage publicly say ‘this is what Israel must accept’, then at that point the pressure on the Israeli government is huge.

But we’re not at that point yet, because the Americans have yet to say what is their substantive view on what Hamas has agreed to.

James Landale

Diplomatic correspondent

We do not know the full details yet of what is included in the proposed Gaza ceasefire deal, including what it says about the idea of a permanent cessation of military operations: Does it mean the war will ultimately end or not?

Because on that point both sides seem still to be in a different position. It’s on that detail that everything matters. And everything that is going on is part of this negotiation.

It’s not just the talks that are taking place either in Doha or in Cairo. The statement that Hamas made yesterday, that is part of the negotiation.

The Israeli statements about what it may or may not do in Rafah are part of the negotiation. The Israeli actions in Rafah are all part of the negotiation.

Each side is trying to put pressure on the other.

Hamas says it has fired rockets at Israeli troops at the Kerem Shalom crossing - the key entry point for humanitarian aid into Gaza from Israel.

The crossing was already closed after a rocket attack by Hamas fighters over the weekend killed four Israeli soldiers in the area.

Hamas's armed wing, which claimed responsibility for Sunday's rocket attack, said in a statement that it had "targeted the gathering of enemy forces" at Kerem Shalom in today's latest attack.

The Israeli Defense Forces posted on X that sirens had sounded in the Kerem Shalom crossing area, after "launches were fired from Gaza".

The Israeli military says it has "operational control" of the Gaza side of the Rafah crossing, and that it has killed 20 Hamas fighters in Rafah overnight.

Yesterday, Israel directed about 100,000 people in the eastern part of Rafah to move to expanded "humanitarian areas" in Khan Younis and al-Mawasi ahead of its offensive.

Rafah's population has grown to 1.4 million people - many of whom have sought refuge there from Israeli offensives in other parts of Gaza. Israel has described the evacuation of eastern Rafah as a "limited and temporary" move.

The al-Mawasi zone is a narrow strip of land with few buildings and largely consists of sandy dunes and agricultural land. Khan Younis and Deir al-Balah are both zones in which Israel has fought, where many buildings have turned to rubble.

Israel's offensive on Rafah, which international leaders warned Israeli PM Benjamin Netanyahu against, is going to cause "a lot of casualties", the EU's foreign policy chief says.

"The Rafah offensive has started again in spite all the requests of the international community, the US, the European Union member states, everybody asking Netanyahu not to attack", Josep Borrell tells reporters.

"I am afraid that this is going to cause again a lot of casualties, civilian casualties. Whatever they say."

Borrell adds that there are "no safe zones in Gaza".

A continuous Israeli bombardment on Rafah has taken place overnight, hours after Israel rejected Hamas's agreement to a ceasefire deal.

Earlier, the IDF said its troops were engaged in a "very targeted operation and a very limited scope against very specific targets" in eastern Rafah.

The Hamas-run health ministry in Gaza says 34,789 Palestinians have been killed in the territory since 7 October, after Israel launched its military campaign in response to Hamas's attacks on southern Israel.

The number of casualties includes at least 54 deaths in the past 24 hours, it says.

The ministry's statement says that 78,204 Palestinians have been injured since 7 October, as the war enters its eighth month.

Hamas gunmen stormed into southern Israel on 7 October, killing about 1,200 people and seizing more than 250 hostages.

Israel has released the following images showing their tanks operating by the Rafah crossing, where the Gaza Strip meets Egypt and through which international aid had been entering the territory:

Hugo Bachega

Reporting from Lebanon

Lebanon is also anxiously watching the negotiations for a possible ceasefire in Gaza which, according to the Shia Islamist group Hezbollah, will mean a pause in the cross-border attacks that the group has carried out on Israel since October.

The violence has led to the displacement of tens of thousands of residents on both sides of the border and raised fears of a major confrontation between Hezbollah and Israel, which fought a devastating month-long war in 2006.

There have been intense efforts, led by US envoy Amos Hochstein, to reduce tensions and reach a long-term deal. Hezbollah, a powerful political and military group supported by Iran, has said it will observe in Lebanon any ceasefire in Gaza, but that a permanent agreement can only be negotiated after the end of the war there.

Hezbollah says its attacks are in support of Hamas, aimed at diverting Israeli troops from Gaza to the border with Lebanon. In Israel, defence officials have threatened to use military force against the group – which, like Hamas, is considered a terrorist organisation by the UK, the US and others – if diplomacy fails to de-escalate the situation.

On Monday, two Israeli soldiers were killed after what Hezbollah described as a drone attack on a military base in the town of Metula. A day earlier, an Israeli airstrike killed four members of a Lebanese family in a house in the village of Meiss al Jabal, according to local officials.

The situation regarding a Gaza ceasefire is "very murky" at the moment, according to international affairs think tank Chatham House.

"I can only imagine how the families of Israel hostages as well as all the people in Gaza are feeling on this rollercoaster," Dr Lina Khatib, an associate fellow at the think tank, tells BBC 5 Live Breakfast.

"Diplomatic efforts are being stepped up by Egypt, by Qatar and by the US. It’s also positive that Benjamin Netanyahu that Israel will send negotiations back to Cairo," she added ahead of talks continuing today.

When asked if any concessions were on the table, she says that it remains unclear.

"There are unconfirmed reports that Hamas effectively wants a long-term end to ‘hostile activity'... if this is long-term or forever as an unnamed Palestinian official supposedly said, this would be a game changing situation because it means Hamas are accepting only playing a political role."

"We’ll have to wait and see," she adds.

Khatib says that Israel wants to put more pressure on Hamas to accept their terms. "Unfortunately, civilians always suffer in this scenario. It is likely still the US is going to exert more pressure on Israel to prevent the current attack on Rafah from expanding," she says.

The significance of Israel taking operational control, as they describe it, of the Gazan side of the Rafah crossing means they have got their soldiers there, it means that they have got their armoured vehicles there.

And it means that they are in control of that area which is the southern route into Gaza.

More broadly, one thing that Israel may be wanting to do is to take control of the entire area, which runs between Gaza and Egypt at the very southern point.

It’s called the Philadelphi Corridor, and Israel says that if it takes control of that it would stop, in the future, tunnels being built in which might give people the chance to smuggle weapons in.

But that’s looking quite a way ahead, because of course at the moment there is all this massive amount of diplomatic activity around the ceasefire talks.

As Israel claims control of the Rafah crossing in Gaza, the UN agency for Palestinian refugees, UNRWA, has warned of the impact diminished aid supplies will have on civilians.

“The biggest problem we have in the last 24 to 48 hours is the border crossing and not having enough aid supplies come in," Louise Wateridge, a spokeswoman for the agency, told BBC Radio 4's Today programme.

The situation is “extremely concerning”, she says.

Looking ahead, she warns of the risk to Gazans' health, saying the sanitation situation is deteriorating and very high temperatures are expected in the summer with many people currently sheltering in plastic tents.

Wateridge, who is in Rafah, says the atmosphere is subdued. Many are waiting to see what happens next, while some are leaving the city, she says.

The Israeli military has said they have taken operational control of the Palestinian side of the Rafah crossing which is on the border with Egypt.

We have witnesses in Rafah saying that there were flares lighting up the sky overnight. There was the constant sound of Israeli bombardments and the Israeli army says it has killed 20 - what it calls Hamas "terrorists" - and says it has found three tunnel shafts in that area around the crossing.

It is stressing at the moment that it is still a very limited and precise operation, that it’s not the full-scale ground offensive of Rafah which the world powers have been warning against because of the dire humanitarian consequences in the city that is so packed with Palestinians who fled the fighting elsewhere in Gaza.

All this going on adds to the diplomatic pressure. The Qataris have been mediators in the potential hostage deal, sending their team back to Cairo so they can talk again about a ceasefire.

It is very confusing because we had an Israeli official saying last night, quoted anonymously, this seems to be an Egyptian proposal that Hamas had accepted, it wasn’t meeting the Israeli requirements.

But then there were other officials coming out and saying, well this is actually very close to an Israeli proposal that was put forward at the end of last month, which the US Secretary of State Antony Blinken then described as being extraordinarily generous.