DOHA/CAIRO (Reuters) -- Gaza cease-fire talks in Doha were paused on Friday with negotiators to meet again next week seeking an agreement to end fighting between Israel and Hamas and free remaining hostages, as Washington cautioned there was much work to be done.
In a joint statement, the U.S., Qatar and Egypt said Washington had presented a new proposal that built on points of agreement over the past week, closing gaps between the sides in a way that could allow rapid implementation of a deal.
Mediators would continue to work on the proposal in coming days, they said.
"The path is now set for that outcome, saving lives, bringing relief to the people of Gaza, and de-escalating regional tensions," they said in the statement.
An Israeli official said its delegation in Doha was heading home later on Friday and that Israeli Prime Minister Benjamin Netanyahu was expected to meet U.S. Secretary of State Antony Blinken on Monday.
The latest round in months of on-off talks to end the war in Gaza, which has killed tens of thousands of Palestinians, began between Israel and mediators on Thursday. The Palestinian militant group Hamas was not directly involved in the talks but was kept briefed on progress.
A senior Hamas official, Izzat al-Rishq, told Reuters that Israel "did not abide by what was agreed upon" in earlier talks, citing what mediators had told them about the result of the talks.
"We believe coming out of Doha this is a positive step forward, but it is just a step forward. There's an awful lot of work that still needs to be done," said White House national security spokesperson John Kirby on television.
Sticking points have included Israel's insistence that peace will only be possible if Hamas is destroyed, and Hamas saying it will only accept a permanent, rather than temporary, cease-fire.
Other difficulties have included the sequencing of a deal, the number and identity of Palestinian prisoners to be released alongside Israeli hostages, control over the border between Gaza and Egypt, and free movement for Palestinians inside Gaza.
Overnight, Israeli forces pounded targets across tiny, crowded Gaza and issued new orders for people to leave areas it had previously designated as civilian safe zones, saying Hamas had used them to fire mortars and rockets at Israel.
The conflict began on Oct. 7 when Hamas fighters rampaged into Israel, killing around 1,200 people and seizing around 250 hostages according to Israeli tallies.
Israel's military campaign has reduced much of Gaza to rubble and killed more than 40,000 Palestinians, mostly civilians, according to Palestinian health authorities. Israel says it has eliminated 17,000 Hamas fighters.
In a statement late on Thursday, Hamas politburo member Hossam Badran said Israel's continuing operations were an obstacle to progress on a cease-fire.
The Israeli delegation included spy chief David Barnea, head of the domestic security service Ronen Bar and the military's hostages chief Nitzan Alon, defense officials said.
The White House sent CIA Director Bill Burns and U.S. Middle East envoy Brett McGurk. Qatari Prime Minister Sheikh Mohammed bin Abdulrahman Al Thani and Egypt's intelligence chief Abbas Kamel were also taking part.
The negotiations took place in the shadow of a feared regional escalation, with Iran threatening to retaliate against Israel after the assassination of Hamas leader Ismail Haniyeh in Tehran on July 31.
With U.S. warships, submarines and warplanes dispatched to the region to defend Israel and deter potential attackers, Washington hopes a cease-fire agreement in Gaza can defuse the risk of a wider war.
Republican U.S. presidential candidate Donald Trump said on Thursday he had told Netanyahu during their last meeting in July to quickly end the Gaza war, but the former president also criticized cease-fire demands.
"He knows what he's doing, I did encourage him to get this over with," Trump told reporters on Thursday. "It has to get over with fast ... Get your victory and get it over with. It has to stop, the killing has to stop."
Netanyahu's office and Trump separately denied on Thursday an Axios report that said they had spoken the previous day about Gaza cease-fire and hostage release talks.
The White House meanwhile said attacks by Israeli settlers on Palestinian civilians in the West Bank were "unacceptable and must stop" after dozens of settlers assaulted a village, killing at least one person.
