International mediators held a new round of talks Thursday aimed at halting the Israel-Hamas war and securing the release of scores of hostages, with a potential deal seen as the best hope of heading off an even larger regional conflict.

The United States, Qatar and Egypt met with an Israeli delegation in Qatar as the Palestinian death toll from the 10-month war climbed past 40,000, according to Gaza health authorities. Hamas, which did not participate directly, accuses Israel of adding new demands to a previous proposal that had U.S. and international support, and to which Hamas had agreed in principle.

White House national security spokesperson John Kirby called the talks an important step and said they’re expected to run into Friday. He said a lot of work remains, given the complexity of an agreement and that negotiators were focusing on its implementation.

A cease-fire in Gaza would likely calm regional tensions. Diplomats hope it would persuade Iran and Lebanon’s militant Hezbollah group to hold off on retaliating for the killings of a top Hezbollah commander in an Israeli airstrike in Beirut and of Hamas’ top political leader in a Tehran explosion.

Kirby warned Iran has made preparations and could attack soon without warning — and that its rhetoric should be taken seriously.

Mediators have spent months trying to hammer out a three-phase plan in which Hamas would release scores of hostages — captured in the Oct. 7 attack that triggered the war — in exchange for a lasting cease-fire, the withdrawal of Israeli forces from Gaza and the release of Palestinians imprisoned by Israel.

Both sides have agreed in principle to the plan, which President Biden announced on May 31. But Hamas has proposed “amendments” and Israel has suggested “clarifications,” leading each side to accuse the other of making new demands it cannot accept.

Gaps remain even after months of talks

Hamas has rejected Israel’s latest demands, which include a lasting military presence along the border with Egypt and a line bisecting Gaza where it would search Palestinians returning to their homes to root out militants. Hamas spokesperson Osama Hamdan told the Associated Press that the group is only interested in discussing the implementation of Biden’s proposal and not in further negotiations over its content.

Prime Minister Benjamin Netanyahu denies Israel has made new demands, but he has also repeatedly raised questions over whether the cease-fire would last, saying Israel remains committed to “total victory” against Hamas and the release of all the hostages.

The most intractable dispute has been over the transition from the first phase of the cease-fire — when women, children and other vulnerable hostages would be released — and the second, when captive Israeli soldiers would be freed and a permanent cease-fire would take hold.

Hamas is concerned that Israel will resume the war after the first batch of hostages is released. Israel worries Hamas will drag out the talks on releasing the remaining hostages indefinitely. Hamdan provided documents showing Hamas had agreed to a U.S. bridging proposal under which talks on the transition would begin by the 16th day of the first phase and conclude by the fifth week.

More recently, Hamas has objected to what it says are new Israeli demands to maintain a presence along the Gaza-Egypt border and a road dividing northern and southern Gaza. Israel denies these are new demands, saying it needs a presence along the border to prevent weapons smuggling and that it must search Palestinians returning to northern Gaza to ensure they are not armed.

The demands were made public only recently. Hamas has demanded a full Israeli military withdrawal, which was also part of all previous versions of the cease-fire proposal, according to documents shared with the AP that were verified by officials involved in the negotiations.

On Thursday, U.S. State Department spokesperson Vedant Patel said the broader framework of the deal laid out by Biden in May has generally been accepted and that the negotiation was a process, which was expected to continue.

‘People have no breath left in them’

The war began when Hamas-led militants stormed across the heavily guarded border Oct. 7 in an attack that shocked Israel’s vaunted security and intelligence services. The militants attacked through farming communities and army bases, killing some 1,200 people, mostly civilians.

They abducted 250 more people. More than 100 hostages were released during a weeklong November cease-fire, and around 110 are believed to still be inside Gaza, though Israeli authorities believe around a third of them have died on Oct. 7 or in captivity. Seven were rescued in military operations.

Israel’s retaliatory offensive has killed 40,005 Palestinians, Gaza’s Health Ministry said Thursday, without saying how many were militants. The offensive has left destruction across the territory and driven the vast majority of Gaza’s 2.3 million people from their homes, often multiple times.

“Oh Lord, we hope they reach an agreement and the war ends, because the population has been annihilated completely,” Abu Nidal Eweini told the AP in the central Gaza city of Deir al Balah. “People have no breath left in them anymore. People are tired.”

Successive evacuation orders and military operations have driven hundreds of thousands of people into a so-called humanitarian zone along the coast where they live in crowded tent camps with few services. Aid groups have struggled to deliver food and supplies, prompting warnings of famine.

Hamas has suffered major losses, but its fighters have repeatedly managed to regroup, even in heavily destroyed areas where Israeli forces had previously operated.

Israel’s military spokesperson, Rear Adm. Daniel Hagari, said Thursday that the army had killed more than 17,000 Hamas militants in Gaza since the start of the war, without providing evidence. He also said the army had dismantled approximately 50 underground tunnels by the strategic Philadelphi Corridor along Gaza’s border with Egypt.

To the north, Hezbollah has traded near-daily fire with Israel along the Lebanon-Israel border in what the Lebanese militant group says is a support front for its ally Hamas. Other Iran-backed groups across the region have also attacked Israeli, American and international targets, drawing retaliation.

Iran and Israel traded fire directly for the first time in April, after Iran retaliated for an apparent Israeli strike on its embassy compound in Syria that killed two Iranian generals. Many fear a repeat after the killing of Hamas leader Ismail Haniyeh, who was visiting Iran for the inauguration of its new president. The explosion was widely blamed on Israel, which hasn’t said whether it was involved.

Hezbollah has meanwhile vowed to avenge the killing of its commander, Fouad Shukur, raising fears of an even more devastating sequel to the 2006 Israel-Hezbollah war.

Still, Iran and Hezbollah say they do not want a full-blown war, and a cease-fire in Gaza could provide an off-ramp after days of escalating threats and a massive military build-up across the region.

Associated Press writer Sewell reported from Doha, Goldenberg reported from Tel Aviv. AP writers Bassem Mroue in Beirut, Wafaa Shurafa in Deir al Balah, Gaza Strip, and Aamer Madhani in Washington contributed to this report.