DEIR AL-BALAH, Gaza Strip — A new swap of hostages held by Hamas for Palestinian prisoners in Israel, including an American released by the terrorist group, got underway late Wednesday in the final hours of the current Gaza truce as international mediators raced to extend the halt of Israel’s air and ground offensive to allow further exchanges.

The Israeli military said a group of 10 Israeli women and children and four Thai nationals had been handed over by Hamas to the Red Cross in Gaza and were heading to exit the territory. Earlier, two Russian-Israeli women were freed by Hamas in a separate release. Israel was set to free 30 Palestinian prisoners in return.

A second American hostage, Liat Atzili, was among those released by Hamas, President Biden told reporters, according to the Hill. Ms. Atzilli is “safe in Egypt just across the border,” Mr. Biden said, adding that he had spoken to her parents, the Hill reported. “Things are moving well,” Mr. Biden added.

Ms. Atzili, a citizen of Israel and America, is a mother of three and lived at Kibbutz Nir Oz, the Hill reported, and she was seized by Hamas on October 7. On Sunday, the Hill added, a 4-year-old American hostage was released by Hamas.

Negotiators were working down to the wire to hammer out details for a further extension of the truce beyond its deadline of early Thursday. The talks appear to be growing tougher as most of the women and children held by Hamas are freed, and the militants are expected to seek greater releases in return for freeing men and soldiers.

International pressure has mounted for the cease-fire to continue as long as possible after nearly eight weeks of Israeli bombardment and a ground campaign in Gaza. Israel has welcomed the release of dozens of hostages in recent days and says it will maintain the truce if Hamas keeps freeing captives.

Still, Prime Minister Netanyahu underscored on Wednesday that Israel will resume its campaign to eliminate Hamas, which has ruled Gaza for 16 years and orchestrated the deadly attack on Israel that triggered the war.

“After this phase of returning our abductees is exhausted, will Israel return to fighting? So my answer is an unequivocal yes,” he said. “There is no way we are not going back to fighting until the end.”

He spoke ahead of a visit to the region planned this week by Secretary Blinken to press for further extensions of the truce and hostage releases.