Negotiations over a Gaza cease-fire and hostage release deal — framed by U.S. officials as a “final stage” bid to end the conflict — resumed Thursday, as local health authorities said the Palestinian death toll in Gaza has passed 40,000.

CIA Director William J. Burns and White House Middle East coordinator Brett McGurk joined Israeli officials, as well as mediating partners from Egypt and Qatar, for fresh talks in Doha aimed at ending the conflict and bringing Israel’s hostages home.

Hamas representatives were not in attendance, Ghazi Hamad, a member of the group’s diplomatic team, confirmed, after its lead negotiator, Ismail Haniyeh, was assassinated during a trip to Tehran last month. In public, Israel has neither confirmed nor denied its role in the killing of the Hamas leader — though it privately told U.S. officials afterward that it was responsible.Regional tensions loom large over this new round of diplomacy, as Iran and the Lebanese Hezbollah group vow to strike Israel in retaliation for Haniyeh’s slaying, as well as that of top Hezbollah commander Fuad Shukr. But there were indications Thursday that resumed peace talks could temporarily allay fresh attacks from across the Lebanese border.“We can say that Hezbollah will not launch its retaliation operation during the Qatar talks because the party does not want to be held accountable for obstructing the talks or a potential deal,” said an individual with close ties to Hezbollah, who spoke on the condition of anonymity because he was not authorized to brief the media. “The retaliation can wait, it is not urgent or has a time limit.”

Hamas says that it will reengage with talks if it receives a “clear commitment” from Israel on its latest proposal. The group has informed mediators that it is willing to meet with them after the Thursday session if there are developments, or a serious response from Israel, according to an official familiar with the negotiations who, like others, spoke on the condition of anonymity to discuss sensitive matters.