Top US diplomat Antony Blinken on Monday said Israel had accepted a US "bridging proposal" for a Gaza truce deal and pressured Hamas to do the same, having earlier said the talks may be the "last opportunity" for a ceasefire.
Blinken, on his ninth visit to the Middle East since the Gaza war started, said he had "a very constructive meeting" with Israeli Prime Minister Benjamin Netanyahu, who "confirmed to me that Israel supports the bridging proposal".
"He supports it. It's now incumbent on Hamas to do the same," Blinken told reporters in Tel Aviv.
Washington put forward the proposal last week after the most recent round of talks in Qatar.
Ahead of those talks, Hamas called on mediators to implement a framework outlined in late May by US President Joe Biden, rather than hold more negotiations.
The movement on Sunday said the bridging proposal "responds to Netanyahu's conditions" and leaves him "fully responsible for thwarting the efforts of the mediators".
Blinken said Netanyahu had "committed to sending his senior expert team" to further negotiations, "but we look to Hamas, first and foremost, to get behind the bridging proposal" which, he said, incorporates the May framework.
Earlier 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."
Months of on-off negotiations with US, Qatari, and Egyptian mediators have failed to produce an agreement
Blinken is due to travel on Tuesday to Egypt where ceasefire talks are expected to resume this week. He said he will then go on to Qatar.
Israel and Hamas have blamed each other for delays in reaching a truce accord that diplomats say could help avert a wider conflagration in the Middle East.
"We're working to make sure that there is no escalation," Blinken said.
Biden said on Sunday that a ceasefire was "still possible" and that the United States was "not giving up".
The Biden administration is under domestic pressure over Gaza. During Blinken's visit to Israel, pro-Palestinian protests took place outside the Democratic National Convention in Chicago, ahead of November's presidential election.
Late on Sunday, hours after Blinken landed in the city, a rare bombing took place in Tel Aviv.
The armed wings of Hamas and Islamic Jihad, another militant group, later claimed the blast and threatened to carry out more such attacks.
One person – the bomber according to Israeli media – was killed and another wounded.
Israeli government spokesman David Mencer said the bombing could have been more serious but the assailant detonated the explosives before managing to reach a more heavily populated area.
It came as Israel and Hamas traded blame for delays in reaching a truce deal.
Hamas insisted on "a permanent ceasefire and a comprehensive [Israeli] withdrawal from the Gaza Strip", saying Netanyahu wanted to keep Israeli forces at several strategic locations within the territory.
Western ally Jordan, captive supporters who protested in Tel Aviv during Blinken's visit, and Hamas itself have called for pressure on Netanyahu in order for an agreement to be reached.
On Sunday, Netanyahu said that Hamas "remains obstinate" and must be pressured, a day after his office said Israeli negotiators had expressed "cautious optimism" about reaching a deal.
US, Qatari, and Egyptian mediators also reported progress.
Far-right members crucial to the prime minister's governing coalition oppose any truce.
Israel's war on Gaza has killed at least 40,139 people, according to the Palestinian enclave's health ministry.
A 7 October attack on southern Israel resulted in the deaths of 1,198 people, according to an AFP tally of Israeli official figures.
Out of 251 captives seized during Hamas-led attack, 111 are still held in Gaza, including 39 the military says are dead.
Netanyahu said on Monday negotiators were aiming to "release a maximum number of living hostages" in the first phase of any ceasefire.
The Biden framework would freeze fighting for an initial six weeks while Israeli and Palestinian captives are exchanged and humanitarian aid enters Gaza.
Fighting raged on in Gaza and along the Israel-Lebanon border where Israeli forces and Hezbollah have traded near-daily fire throughout the war.
Israel struck Hezbollah weapons depots deep in Lebanon's east, in the Bekaa area, a source close to the group told AFP. Most exchanges of fire have been along the Israel-Lebanon border, though Israel has previously struck the Bekaa valley.
An Israeli soldier and two Hezbollah fighters were killed in cross-border clashes, the Israeli military and Hezbollah said on Monday.
In southern Gaza, a medical source told AFP three people were killed in Abassan village and witnesses reported Israeli airstrikes near the Islamic University in Khan Younis.
The Israeli military said troops had "expanded" operations in Khan Younis and the outskirts of Deir Al-Balah, central Gaza. A medical source told AFP a baby girl was killed in airstrikes west of Khan Younis.
The Israeli war has devastated Gaza. A video posted to social media by a UN official showed a convoy passing scenes of utter destruction with almost every building reduced to rubble and the few still standing badly damaged.
What little remains of the health system is under intense pressure and last week Gaza recorded its first polio case in 25 years.
Blinken said on Monday that Washington was working with Israel and expected they would have a vaccination plan "in the coming weeks".
The UN says it has one ready to go that would require two week-long pauses in the fighting.