The C.I.A. director, William J. Burns, met in Warsaw on Monday with Israeli and Qatari officials for talks aimed at restarting hostage and prisoner exchanges, according to U.S. officials.

Under a weeklong truce between Israel and Hamas last month, 105 hostages were freed in exchange for the release of 240 Palestinians from Israeli jails before negotiations broke down and the war resumed on Dec. 1. Since then, American officials have pushed various proposals aimed at continued humanitarian releases or other exchanges.

Pressure for another agreement has mounted in recent days, after the Israeli military said on Friday that its soldiers had fatally shot three unarmed men who turned out to have been hostages. Hamas had not released any videos of its hostages since before the exchanges began. But on Monday it posted one on social media showing three older men, one of whom pleaded for their release.

Resuming talks has been complicated, with deeper differences over the terms of further exchanges.

After the deal fell apart, a U.S. official said publicly that Hamas “reneged” on an agreement to release all female hostages. A Hamas official said it considered some of the remaining female hostages to be soldiers.

Israeli officials, speaking on the condition of anonymity, said Hamas failed to release as many hostages as promised, while making more demands. Hamas had been proposing deals that would release more Palestinians from Israeli jails, including higher-profile detainees. Israeli officials insisted they wanted all women and children released before discussing further exchanges.

There are some reasons to think that new talks may be fruitful. After the accidental deaths of the three hostages, the Israeli government is under more pressure to secure the release of the remaining people being held by Hamas and its allies in Gaza. The United States is also increasing pressure on Israel to scale back its major combat operations in Gaza and transition to a new phrase in the war.

Mr. Burns met with David Barnea, the head of Mossad, Israel’s spy agency. Mr. Barnea has been leading the Israeli negotiation efforts, and the White House tapped Mr. Burns to work with him.

The two men spoke in Warsaw with Prime Minister Mohammed bin Abdulrahman Al Thani of Qatar. The Qataris host Hamas’s political wing in Doha and have been working to facilitate negotiations.

Neither Israel nor the U.S. speak directly to Hamas leadership, but instead work through the Qataris.

The video released by Hamas on Monday showed three men, bearded and seated, with one of the men speaking to the camera and identifying himself as a 79-year-old from Kibbutz Nir Oz. The video includes subtitles in English that do not directly correspond to the Hebrew words used by the hostage.

The Israeli government and military have previously dismissed these videos as “psychological warfare.”

The resumption of talks was earlier reported by Axios. A spokeswoman for the C.I.A. declined to comment, citing the agency’s policy of not discussing the travel of the director.

Ephrat Livni contributed reporting.