President Biden’s Middle East coordinator, Brett McGurk, will meet with Egyptian and Qatari leaders in hopes of making progress toward freeing captives held by Hamas.

A senior Biden administration official is heading back to the Middle East on Sunday in hopes of making progress toward an agreement that would result in the release of more hostages held by Hamas in exchange for a pause in Israel’s military campaign in the Gaza Strip, two American officials said.

President Biden’s Middle East coordinator at the White House, Brett McGurk, will travel to Cairo to meet with Gen. Abbas Kamel, the chief of Egypt’s General Intelligence Service and widely considered the nation’s second most powerful official, according to the American officials, who spoke on the condition of anonymity because of the sensitivity of diplomatic talks. Mr. McGurk will later head to Doha, Qatar, to meet with the country’s prime minister, Mohammed bin Abdulrahman bin Jassim al-Thani.

Egyptian and Qatari leaders have been important players in hostage talks and helped broker a cease-fire in November during which Hamas released more than 100 people from captivity.

The trip by Mr. McGurk comes as Israel’s prime minister, Benjamin Netanyahu, said once again that he would not meet Hamas’s demands of a withdrawal of Israeli forces in return for the release of hostages. “Let it be clear: I utterly reject the Hamas monsters’ capitulation terms,” Mr. Netanyahu said in a statement on Sunday.

Israeli officials say about 240 people were taken hostage during the Oct. 7 attack on Israel led by Hamas, which also killed about 1,200 people. But divisions have emerged in Israel over the path forward, with some citizens protesting the government’s failure to secure the hostages’ release, including a group that gathered near Mr. Netanyahu’s Jerusalem home on Sunday, according to Israeli media. Doubts have also emerging among military leaders that fighting alone could achieve their safe return; Gadi Eisenkot, a former army chief who is serving in the war cabinet, said in a television interview last week that it was an “illusion” to believe that the hostages could be safely secured through military operations.

Mr. McGurk’s trip, which was previously reported by Axios, comes just days after Israel and Hamas agreed through Qatari intermediaries to allow medicine to be delivered to hostages in exchange for additional medicine and aid for civilians in Gaza.

But American officials have said a new hostage release has been complicated by Hamas’s evident desire for a permanent cease-fire, rather than the kind of temporary pause that accompanied the releases in November.

Administration officials said the hostages were just one of several topics arising from the Israel-Hamas war that Mr. McGurk will address on his travels to the region. Mr. Netanyahu has also grown increasingly vocal in pushing back against Mr. Biden’s insistence that Israel ultimately negotiate the creation of a Palestinian state in exchange for guarantees of its own security.

Mr. Netanyahu publicly rejected the idea again this weekend, after speaking with Mr. Biden on Friday about the issue of a two-state solution, saying on Sunday that all territory west of the Jordan River must be under “full Israeli security control.”