Top US diplomat Antony Blinken was in Egypt on Tuesday for talks on a Gaza ceasefire after saying Israel had accepted a US "bridging proposal" for a deal and urging Hamas to do the same.
Blinken, on his ninth visit to the Middle East since the Palestinian militant group's October 7 attack triggered the war with Israel, flew to El Alamein, the Mediterranean city famous for a World War II battle, and began talks with Egyptian President Abdel Fattah al-Sisi at his summer palace.
Afterwards, he will head to a meeting with Qatar's emir, Sheikh Tamim bin Hamad Al-Thani, in Doha, the scene of ceasefire talks last week.
Both Egypt and Qatar are working alongside the United States to broker a truce in the 10-month Gaza conflict.
Washington put forward the latest proposal last week aimed at after the talks in Doha.
Blinken said Monday he had "a very constructive meeting" with Israeli Prime Minister Benjamin Netanyahu, who "confirmed to me that Israel accepts the bridging proposal".
Ahead of those talks, Hamas called on the mediators to implement the framework set out by US President Joe Biden in late May, rather than hold more negotiations.
The movement said on Sunday that the current US proposal "responds to Netanyahu's conditions".
At the weekend, Hamas political bureau member Sami Abu Zuhri said US optimism about the prospects for the deal was an "illusion".
On Monday, the US secretary of state had said: "This is a decisive moment -- probably the best, maybe the last, opportunity to get the hostages home, to get a ceasefire and to put everyone on a better path to enduring peace and security".
Israel and Hamas have blamed each other for delays in reaching an accord that diplomats say would help avert a wider conflagration in the Middle East that could draw in Iran and Hezbollah in Lebanon.
Fears of an escalation have mounted since Hezbollah and Iran vowed to respond after an Israeli strike on Beirut last month killed a top Hezbollah commander, Fuad Shukr, shortly before an attack in Tehran blamed on Israel killed Hamas political leader Ismail Haniyeh.
Hezbollah said it launched rocket salvos at Israeli army positions in the annexed Golan Heights, in the latest of the cross-border exchanges which have raged almost daily since the Gaza war began.
"There is, I think, a real sense of urgency here, across the region, on the need to get this over the finish line and to do it as soon as possible," Blinken said.
The Biden administration is under domestic pressure over Gaza, with pro-Palestinian protests taking place outside the Democratic National Convention in Chicago on Monday.
He acknowledged Hamas objections to the latest draft. "It's still in play, but you can't predict," he said as he prepared to leave Chicago.
"Israel says they can work it out... Hamas is now backing away."
Israeli military operations in Gaza have continued throughout the truce talks.
Gaza's civil defence agency said an Israeli strike hit a school housing displaced Palestinians and killed seven people. The Israeli military said it struck a Hamas command centre.
Medics reported six dead in two separate Israeli air strikes in and around the southern city of Rafah.
Western ally Jordan, hostage supporters who protested in Tel Aviv during Blinken's visit, and Hamas itself have called for pressure on Netanyahu for an agreement to be reached.
Far-right members crucial to the prime minister's governing coalition oppose any truce.
The October 7 attack on southern Israel resulted in the deaths of 1,198 people, mostly civilians, according to an AFP tally of Israeli official figures.
Israel's retaliatory offensive in Gaza has killed at least 40,173 people, according to the territory's health ministry, which does not give details of civilian and militant deaths.
Out of 251 hostages seized during Hamas's attack, 105 are still held in Gaza, including 34 the military says are dead.
The Biden framework would freeze fighting for an initial six weeks while Israeli hostages are exchanged for Palestinian prisoners in Israeli jails and humanitarian aid enters Gaza.
Netanyahu said on Monday that negotiators were aiming to "release a maximum number of living hostages" in the first phase of any ceasefire.
The Israeli military said it had retrieved the bodies of six hostages from the southern Gaza district of Khan Yunis in a joint operation with internal security agency Shin Bet.
The hostages were Yagev Buchshtab, Alexander Dancyg, Yoram Metzger, Nadav Popplewell, Chaim Perry, previously announced dead, and Avraham Munder, whose kibbutz of Nir Oz near Gaza announced his death earlier Tuesday.
Campaign group the Hostages and Missing Families Forum called on the government to ensure the remaining hostages are returned to Israel in a negotiated deal.
"The Israeli government, with the assistance of mediators, must do everything in its power to finalise the deal currently on the table," it said.
