Rafah’s fate hung in the balance on Monday after Hamas said it had accepted a ceasefire-for-hostage deal but Israel responded sceptically and said it would press on with its campaign on Gaza’s southernmost city, carrying out night airstrikes. The more than 1 million Palestinians taking refuge in Rafah were thrown into confusion by the day’s events. Israel issued orders for the evacuation of part of the city earlier on Monday, triggering an exodus of thousands of people. There were celebrations in the streets in the evening as Hamas’s announced it had accepted ceasefire, but then disappointment and bewilderment when Israel gave a tepid response and began bombing. The Israeli military said late on Monday it was conducting targeted strikes against Hamas in Rafah. Israel’s prime minister, Benjamin Netanyahu, said the terms that Hamas had agreed to fell far from meeting his government’s demands but he would dispatch a delegation for further negotiations through Egyptian and Qatari mediators. The war cabinet said it would pursue the operation in Rafah to “exert military pressure on Hamas in order to advance the release of the hostages and other goals of the war”. One Israeli official said it was unclear exactly which proposal Hamas was accepting, as some of the terms appeared to differ substantially from those shown by mediators to Israel and agreed by the Israeli government last week. “[We] don’t recognise some,” the official, speaking on condition of anonymity, said. Despite the late hour, hundreds of Israelis converged on the main military headquarters in Tel Aviv calling for a deal now. Smaller gatherings were reported in Jerusalem and other cities across Israel. “Hamas’s announcement must pave the way for the return of the 132 hostages held captive by Hamas for the past seven months. Now is the time for all that are involved to fulfil their commitment and turn this opportunity into a deal for the return of all the hostages,” a statement from the Hostages Families Forum said. “We continue to believe that a hostage deal is in the best interests of the Israeli people; it’s in the best interest of the Palestinian people,” the US state department spokesperson, Matthew Miller, said. “It would bring an immediate ceasefire, it would allow increased movement of humanitarian assistance and so we’re going to continue to work to try to reach one.” The UN secretary-general, António Guterres, urged Israel and Hamas “to go the extra mile needed to make an agreement come true and stop the present suffering”, according to his spokesperson, Stephane Dujarric. The main difference dividing the two sides at the talks in Cairo last week was over the permanence of a ceasefire. Israel wants to reserve the right to resume military action, particularly against the remnants of Hamas’s military wing in Rafah, after the ceasefire has run its course. Talks in Cairo had appeared to stall over Hamas’s insistence that Israel should commit to making the ceasefire permanent at the outset of the agreement, rather than to negotiate its duration after the truce had taken hold. An account in Haaretz suggested that the Hamas version does not include an immediate demand for a permanent ceasefire, but also changes other elements of the Egyptian deal proposal, such as the requirement it free 33 hostages in the first phase. It also reportedly takes away Israel’s right of veto on which Palestinian detainees are released in exchange. Hamas officials were quoted as saying the plan they had accepted involved a ceasefire, reconstruction of Gaza, return of displaced people to their homes and a prisoner swap deal, and that the deal would involve three phases, each of 42 days each. That description left it unclear whether there were substantial differences to the proposal put on the table by Egyptian mediators last week. As a potential ceasefire hung in the balance, witnesses described frightened families leaving Rafah on foot, riding donkeys, pushing trolleys or packing their belongings into overloaded trucks hours after reading leaflets dropped by the Israeli military that told residents and displaced people in eastern neighbourhoods to flee. “An Israeli military offensive will lead to an additional layer of an already unbearable tragedy for the people in Gaza,” said Philippe Lazzarini, the head of Unrwa, the UN relief agency in the region. “It will make even more difficult to reverse the expansion of the already man-made famine.” Joe Biden, the US president, spoke to Benjamin Netanyahu, Israel’s prime minister, on Monday afternoon and “reiterated his clear position” on Rafah, the White House said. US officials have repeatedly said Israeli has to present an adequate humanitarian plan for the more than 1 million Palestinians who have sought shelter in Rafah, and that the US would change its policy on the region if Israel went ahead with an offensive in the absence of such a plan. Officials made clear on Monday that no such plan was possible in the current circumstances, so the US opposition to a Rafah attack was not likely to soften. It will be up to Biden to decide whether a US policy change would involve restrictions on arms supplies. US officials refused to comment on a report on the Axios news site that a delivery of US-made ammunition due to ship last week had been put on temporary hold. The Israel Defense Forces (IDF) said they had broadcast instructions through “announcements, text messages, phone calls and media broadcasts in Arabic” telling an estimated 100,000 residents of an eastern section of Rafah to head to an “expanded humanitarian zone” on the coast and around the badly damaged city of Khan Younis. “This is an evacuation plan to get people out of harm’s way,” an Israeli military spokesperson said. “This is limited in scope and not a wide-scale evacuation of Rafah.” The Biden administration agrees with the UN and aid agencies that there is no safe area for the people in Rafah to escape to, given the wholesale destruction of Gaza after seven months of Israeli bombardment. While the Israelis say the section of Rafah under evacuation orders is limited with an estimated population of 100,000, US officials think any military operation in that district would have a knock-on effect, terrifying many others across Rafah to flee. Rafah has been sheltering more than 1 million people displaced from elsewhere in Gaza during the war and is a key logistics base for humanitarian operations across the territory. Dense tent encampments surround the city and have also already crowded al-Mawasi, the coastal zone about 3 miles north-east to which Israel has told people to evacuate. Khan Younis is considered “completely uninhabitable” by aid workers. A rocket barrage launched by Hamas on Sunday from Rafah against a military base near the Kerem Shalom checkpoint, which killed four soldiers, may have spurred the Israeli decision. US officials also said that the targeted checkpoint was the main crossing point for humanitarian deliveries into Gaza. Israeli officials have repeatedly said a “decisive victory” requires the destruction of a substantial Hamas combat force they say is based in Rafah, and the capture or killing of top Hamas leaders thought be sheltering in tunnels under the city, possibly with dozens of hostages. Humanitarian officials and displaced people already living in al-Mawasi describe acute overcrowding, inadequate food, limited fresh water and an almost total absence of sanitation. Israeli forces have bombarded targets in al-Mawasi at least twice in recent months. Aid officials have long warned of massive disruption to the effort to stave off famine in Gaza in the event of a major Israeli offensive in the south. Any attack on Rafah would lead to “the collapse of the aid response”, the Norwegian Refugee Council said on Monday. Netanyahu has been under domestic pressure to make concessions to obtain the release of the hostages in Gaza but appears so far to have prioritised the demands of far-right parties, which have threatened to withdraw crucial support for his coalition if a ceasefire deal is signed now. Israel’s far-right national security minister, Itamar Ben-Gvir, wrote on X: “Hamas’ exercises and games have only one answer: an immediate order to occupy Rafah! Increasing military pressure, and continuing the complete defeat of Hamas, until its complete defeat.”