Israeli Prime Minister Menahem Begin and Egyptian President Anwar Sadat will meet in Egypt on Christmas Day to discuss Israel's peace proposal, Begin said today.

The Israeli leader expressed the hope that if an agreement is reached at the Suez Canal city of Ismailia, he and Sadat will agree to accept an invitation from President Carter to fly to Washington where the three leaders could jointly make the agreement's terms known.

Such a three-way meeting could be held in the new year if all goes well, Begin told reporters in his Waldorf Towers suite on the last day of his visit to the United States.

Begin spent much of the day resting and conferring with advisers, but he also kept up the momentum of the astonishing rapprochement between Egypt and Israel, begun by Sadat's Nov. 19 trip to Israel, through three television interviews and brief meetings with other reporters.

"Sunday is Christmas," Begin said of the timing of his upcoming second meeting with Sadat, "but the Christian world, I hope, will approve because [the meeting] is for peace."

Ismailia was chosen partly for security reasons and partly because Sadat has a guest house there to which he frequently retreats.

This morning, Begin expected to meet Sadat the day after Christmas, but early today Sadat gave a message to U.S. Ambassador to Egypt Hermann F. Eilts proposing that the visit be Christmas Day.

Eilts relayed the message to Secretary of State Cyrus R. Vance, who passed it to Israeli Ambassador to the United States Simcha Dinitz. Begin quickly accepted the new date.

Begin has refused to reveal the full details of his peace proposals publicly before he presents them to Sadat, but many of them have leaked, and Begin announced one of the principal Israeli offers Sunday - autonomy for the Palestinian Arabs on the West Bank of the Jordan River, which Israel captured from Jordan in the 1967 war.

Begin elaborated on his plan in an interview with ABC's Barbara Walters today. "We will give the residents completely free option of choice of citizenship, either Israeli citizenship or Jordanian citizenship," Begin said. West Bank residents could choose to carry the passport of either nation, he added.

Although the Begin and Sadat moves toward peace have made them enormously popular figures, Begin sought no public appearance here, remaining in his hotel headquarters and relying on television to keep him and the peace talks in the news.

"They know how to use the three networks," an Israeli remarked of Begin and Sadat.

Israeli diplomats and journalists traveling with the prime minister were openly delighted with Begin's Washington visit and the continuing movement toward some sort of agreement with Egypt.

"He cannot fail now," one diplomat said. "The first meeting with Carter was touched by the wings of history. After Begin's plan began to be laid out and I saw the expressions of the people in the room, I thought that 30 years of war were ending right there."

Begin's first official meeting today was with a delegation of Lebanese-American Christians who came to thank him for his government's military and medical assistance to Christians in southern Lebanon.

It was the first group of Arab-Americans ever to request a meeting with an Israeli Prime Minister, and Israeli spokesman said.

Dr. Elias Saadi, Paul Cory and Anthony Abraham also expressed support for the efforts of Begin and Sadat to make peace, the spokesman said.

Begin are interview to Israeli television, Walters and NBC's John Chancellorand met with Rabbi Alexander Schidler and Dr. Yehuda Helman, leaders of the Conference of President of Major American-Jewish Organizations.

In the late afternoon, Begin received House Majority Leader Jim Wright (D-Tex.). An Israeli spokesman said that Begin's Washington schedule had been so rowded he had been unable to meet house leaders. Minority Leader John J. Rhodes (R-Ariz.) was expected, but did not arrive for the meetings.

In Washington, Begin had briefed Senate leaders, former President Ford and former secretary of State Henry Kissinger on his proposals, in adddition to discussing them with the Carter administration.

His last official appointment was with U.N. Secretary General Kurt Waldheim, Begin said that a role would be found for the United Nation in the movement toward peace that has so far left the world organization on the sidelines.

Israeli officials said, however, that Waldheim would not be given full details of the Israeli peace plan because of Begin's desire not to have government other than the United States and his European allies know the plan until after he presents it to Sadat.

Begin left tonight aboard a regularly scheduled El Al flight for London.