Israelis and Palestinians prepared on Sunday for an exchange of all the living hostages who remain in Gaza for about 2,000 Palestinians imprisoned by Israel, the cornerstone of a new cease-fire agreement.

The Israeli government said the exchange was expected to begin on Monday morning local time, but Israel was prepared for it to happen even sooner.

On both sides, there was a sense of relief mixed with elation over the progress after two years of devastating war. Adding to that optimism, the open-ended truce between Israel and Hamas, which was brokered by the United States and Arab mediators and began at noon on Friday, appeared to be holding over the weekend.

As part of the first phase of the cease-fire deal, Israeli forces have already withdrawn to a new defensive line inside Gaza. Thousands of displaced Palestinian residents have headed back to Gaza City in the north of the territory, and increased quantities of desperately needed food, medicine and other humanitarian aid are expected to start flowing into the enclave.

President Trump was expected to leave the United States on Sunday and land in Israel on Monday for a short visit. He is set to meet with the families of hostages and address the Israeli Knesset, or parliament, in Jerusalem.

He then is scheduled to fly to Sharm el-Sheikh, a Red Sea resort in Egypt, where he and President Abdel Fattah el-Sisi of Egypt will chair a summit with other Arab partners who supported the deal. World leaders have been invited to attend, but it was not immediately clear whether any Israeli or Palestinian representatives will participate.