The C.I.A. director met with top Qatari and Egyptian officials on Wednesday as the Biden administration launched a renewed push for a cease-fire in Gaza, though Israel and Hamas appeared to remain far apart on the latest proposal to pause the fighting.

The U.S. spy chief, William J. Burns, met in Doha, Qatar, with the Qatari prime minister, Mohammed bin Abdulrahman Al Thani, and the Egyptian intelligence chief, Abbas Kamel, according to an official briefed on the matter, who spoke on the condition of anonymity to discuss the closed-door encounter.

Egypt and Qatar have been key mediators in the talks between Israel and Hamas, which do not talk directly to each other. By dispatching Mr. Burns, the Biden administration signaled that it was still investing heavily in trying to broker a cease-fire to end the bloodshed in Gaza and calm broader regional tensions.

The meeting focused on finding ways to bring Israel and Hamas closer to an agreement, according to the official, who said that Qatar had received preliminary positive feedback from Hamas to a cease-fire proposal endorsed last week by President Biden, but was still waiting to receive a formal response.

On Wednesday, the Qatari prime minister and Mr. Kamel also met with Hamas leaders to discuss the proposal, the official briefed on the talks said.

Mr. Biden described the proposal as a new Israeli offer that would begin with a six-week halt in fighting and ultimately lead to the “cessation of hostilities permanently,” raising hopes among Israelis and Palestinians that a deal to end the nearly eight-month war was finally imminent. But since the president went public with the offer, Prime Minister Benjamin Netanyahu of Israel has repeatedly rejected ending the war without first destroying Hamas’s governing and military capabilities.

On Wednesday, a senior Hamas official repeated the group’s position that it would not agree to any deal that did not provide for a permanent cease-fire. The official, Bassem Naim, said that “it doesn’t make sense” for the group to negotiate while Israeli forces launch fresh attacks in Gaza, and said Hamas would not accept a temporary truce.

“The thirsty will drink a little and the hungry will eat a little, and then after a month and a half we will return to being killed?” he said.

The official briefed on the meeting in Qatar said that recent statements by Mr. Netanyahu and other Israeli officials have made Hamas officials question whether Israel wants a permanent halt in the fighting.

A spokesman for the Qatari Foreign Ministry, Majed al-Ansari, said on Tuesday that it was “waiting for a clear Israeli position that represents the entire government.”

Amid the public disagreements, Mr. Burns’ stay in Doha wasn’t expected to bring about major progress, said a second person briefed on the negotiations, who spoke on condition of anonymity to discuss the sensitive diplomacy. Yahya Sinwar, the Hamas leader in Gaza and the presumed mastermind of the Oct. 7 terrorist attack on southern Israel, still had to weigh in on the latest proposal, that person said.

Brett McGurk, the White House’s Middle East coordinator, was also returning to the region this week for meetings in Cairo, a U.S. official said.

Jake Sullivan, the U.S. national security adviser, said on Wednesday that the proposal outlined by Mr. Biden was “still a live proposal,” even though Mr. Netanyahu has not publicly endorsed it and two of his ministers have said they would oppose any deal that leaves Hamas intact.

“Israel is a raucous democracy, so there is a lot of talk and a lot of chatter,” Mr. Sullivan said in an interview on NBC’s “Today” show. “But the Israeli government has reconfirmed repeatedly, as recently as today, that that proposal is still on the table and now it’s up to Hamas to accept it. And the whole world should call on Hamas to accept it.”

The first phase of the proposal laid out by Mr. Biden called for both sides to observe a temporary six-week cease-fire while they continue to negotiate to reach a permanent one. In a meeting with Israeli lawmakers on Monday, Mr. Netanyahu expressed openness to a 42-day pause in the fighting, embracing at least part of the first phase of the three-part plan described by Mr. Biden, according to a person who attended the discussion.

At a news conference on Tuesday, Osama Hamdan, a Hamas spokesman, said the most recent Israeli position communicated to the group didn’t include a permanent cease-fire or a complete withdrawal of Israeli forces from Gaza, both terms that Hamas has insisted on. Israel, Mr. Hamdan said, was interested in only a temporary cease-fire to free hostages, and would then resume the war.

“We call on the mediators to get a clear position from the Israeli occupation,” he said.

Raja Abdulrahim contributed reporting.