Israel and Hamas appeared to be close to an agreement to declare a ceasefire in Gaza and release hostages held there after more than 15 months of war, the Qatari government said on Tuesday.

The mediators “managed to minimize many disagreements between both sides,” Majed al-Ansari, a spokesman for Qatar’s foreign ministry, told reporters. Tuesday’s talks focused on “the final details of reaching an agreement,” he said.

The talks, which are being brokered by Qatar, Egypt and the United States, come after months of unsuccessful attempts to make progress. In recent weeks, officials familiar with the negotiations have expressed growing hope that a deal is possible, spurred by a looming deadline: the end of President Biden’s term and the Jan. 20 inauguration of President-elect Donald J. Trump.

Mr. Trump warned that there will be “ALL HELL” unless the hostages are released by the time he becomes president. Officials in the Biden administration was pressed for a deal that would become part of the outgoing president’s legacy.

If Hamas and Israel strike a deal, it would bring respite to Palestinians in Gaza, who have endured squalid conditions in displacement camps and relentless Israeli bombing, and to the families of hostages kidnapped from Israel, who have worried for more than a year about the fate of their loved ones. The diplomat said Tuesday’s talks focused on resolving outstanding issues, while a Palestinian in contact with Hamas officials said they would focus on the details of how to implement the agreement. Both spoke on condition of anonymity to discuss sensitive diplomacy.

The emerging agreement, the diplomat said, was largely inspired by previous proposals discussed in May and July.

Mediators and officials have repeatedly warned that even significant progress could be cut short at the last minute. Israel and Hamas have held numerous rounds of talks over the past few months, each of which has ended in recriminations.

“We believe we are in the final stages, but until we have an announcement — there will be no announcement,” said Mr. al-Ansari, adding that there is no immediate timeline for signing the contract.

For more than a year, international efforts have failed to end the Gaza war, which erupted in an October 2023 attack led by Hamas that killed around 1,200 people and took 250 hostages in Gaza, according to Israeli authorities. Israel has launched a military campaign against Hamas that has destroyed large areas of the enclave and killed at least 45,000 people, according to Gaza health officials, who do not distinguish between civilians and fighters.

The office of Benjamin Netanyahu, Israel’s prime minister, confirmed on Tuesday that the delicate negotiations were continuing, but declined further comment.

Israeli officials told reporters Monday night that they believed they were close to reaching an agreement. That optimism was echoed by Mr. Biden in a speech in which he said the cease-fire and hostage agreement was “on the brink” of “finally coming to fruition.”

William J. Burns, director of the CIA, and Brett McGurk, a senior White House official, toured the Middle East seeking progress in the negotiations. Steve Witkoff, Trump’s pick for Middle East envoy, also traveled to Qatar and Israel, meeting with top officials there.