Negotiators were to meet in the Qatari capital Doha again on Friday in an effort to hammer out a Gaza ceasefire agreement as Israel continued to slam targets in the Palestinian enclave.
Gaza health officials reported separately on Thursday that the death toll there had surpassed 40,000 people after more than 10 months of fighting.
This round of negotiations opened on Thursday, and the talks would resume on Friday for a second day, Qatari and US officials said.
A US official briefed on the discussions in Doha, who declined to be identified, told Reuters that Thursday's talks were "constructive."
"This is vital work. The remaining obstacles can be overcome, and we must bring this process to a close," US national security spokesperson John Kirby told reporters at the White House.
Israel, meanwhile, pressed its assault on Gaza. Gaza health officials said at least six Palestinians were killed on Thursday night in an Israeli air strike on a house in Jabalia in northern Gaza Strip.
Israeli troops earlier hit targets in the southern cities of Rafah and Khan Younis.
In a statement issued late on Thursday on Telegram, Hamas politburo member Hossam Badran said Israel's continuing operations were an obstacle to progress on a ceasefire. Hamas officials did not join Thursday's talks.
Badran said the talks must move toward implementation of a framework agreement accepted previously and achieve a complete ceasefire, withdrawal of Israeli forces, return of displaced Palestinians and a hostage exchange deal.
"Hamas looks at the ongoing negotiations in Doha regarding a ceasefire and a hostage exchange from a strategic perspective with the goal of ending the aggression on Gaza," he added.
Mediators planned to consult with Hamas' Doha-based negotiating team after the meeting, the US official told Reuters.
The Israeli delegation includes 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 US Middle East envoy Brett McGurk. Qatari Prime Minister Sheikh Mohammed bin Abdulrahman Al Thani and Egypt's intelligence chief Abbas Kamel also took part.
The negotiations, an effort to end bloodshed in Gaza and bring 115 Israeli and foreign hostages home, were put together as Iran appeared poised to retaliate against Israel after the assassination of Hamas leader Ismail Haniyeh in Tehran on July 31.
ESCALATION RISK
With US warships, submarines and warplanes dispatched to the region to defend Israel and deter potential attackers, Washington hopes a ceasefire agreement in Gaza can defuse the risk of a wider regional war.
The White House said late on Thursday 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.
With US presidential elections looming on Nov. 5, Republican candidate Donald Trump criticized the Biden administration's months-long calls for a ceasefire, saying it "would only give Hamas time to regroup."
Israel and Hamas have each blamed the other for failure to reach a deal yet neither side has ruled out an agreement.
On Wednesday, a source in the Israeli negotiating team said Prime Minister Benjamin Netanyahu has allowed significant leeway on a few of the substantial disputes.
Gaps include the presence of Israeli troops in Gaza, the sequencing of a hostage release and restrictions on the free movement of civilians from southern to northern Gaza.
UN human rights chief Volker Turk said the Gaza death toll of more than 40,000 reported by the enclave's health ministry was a "grim milestone for the world".
Separately, Israel's military said it had "eliminated" more than 17,000 Palestinian fighters in its Gaza campaign.
In shattered Gaza where the war has driven almost all of its 2.3 million population from their homes, there was a desperate desire for an end to the fighting.
"We are hopeful this time. Either it's this time or never I am afraid," Aya, 30, sheltering with her family in Deir Al-Balah in the central part of the Gaza Strip, told Reuters via a chat app.
The war started after a Hamas raid on southern Israel on Oct. 7 in which Israel says Hamas killed some 1,200 people, prompting Israel to attack Gaza in retaliation.
