Israeli and American negotiators are scheduled to return to Qatar over the weekend in an effort to revive cease-fire talks between Israel and Hamas, the Israeli prime minister’s office said on Thursday.

But the announcement came amid new Israeli bombardment both in the Gaza Strip and in Lebanon on Thursday, and uncertainty from U.S. and Qatari officials about whether Hamas might soon rejoin the talks.

“We haven’t yet really determined whether Hamas is prepared to engage,” Secretary of State Antony J. Blinken said at a news conference in Doha, the Qatari capital. “The fundamental question is: Is Hamas serious?”

Mr. Blinken met for an hour with Mohammed bin Abdulrahman Al Thani, Qatar’s prime minister and foreign minister, discussing how to end the wars in Gaza and Lebanon. Appearing together afterward at the news conference, they said they had no indication that Hamas was more willing to negotiate since Israel killed its leader, Yahya Sinwar, last week.

The office of Prime Minister Benjamin Netanyahu of Israel said that David Barnea, the head of the country’s Mossad foreign intelligence service, would depart on Sunday to a meeting in Doha with Mr. Al Thani and William J. Burns, the director of the C.I.A.

Before leaving Qatar for London on Thursday, Mr. Blinken announced that the United States would provide an additional $135 million in humanitarian assistance for “Palestinians in Gaza, in the West Bank as well as in the region” and said the current humanitarian crisis in Gaza was especially urgent with winter approaching.