Israeli Prime Minister Menahem Begin will confer with President Carter here Friday on "the latest developments in the search for peace in the Middle East," the White House announced last night.

The unexpected visit by Begin to Washington, two days after the opening of Egyptian-Israeli peace talks in Cairo, was prposed by Begin on Saturday and quickly accepted by Carter, U.S. officials said.

Begin wants to discuss with Carter "bold" and "positive" Israeli responses to the peace overtures of Egyptian President Anwar Sadat, according to a senior U.S. official accompanying Secretary of State Cyrus R. Vance on his trip to the Middle East.

The Begin-Carter talks will cover the main issues of substance in the Arab-Isreali conflict, reporters were told in Damascus, Syria, by Under Secretary of State Philip C. Habib, Washington post staff writer Ronald Koven reported from Damascus.

This will include the nature of the peace to be estblished. Begin's views on the settlement of the Palestinian problem, and the extent of Israeli withdrawal from war-occupied territories, Habib told reporters.

In Washington, however, senior administration official cautioned reporters against interpreting Begin's trip as signifying either a "crisis or problem" or "an indication of some momentous breakthrough." Instead, it was said, Begin's trip represents "a process of consultation and a positive development."

Begin apparently ewants to demonstrate that the United States and Israel are in basic accord on the stategy for peace initiated by Sadat's dramatic visit to Jerusalem last month.

Since tha breakthrough, Carter administration policy, to the high satisfaction of Begin and Sadat, has shifted away from a conference in Geneva between Israel and ail the Arab nations as the takeoff point for peace negotiations. The United States now supports the Egyptian-Isreali talks in Cairo as the new center of Middle East diplomacy.

Begin is due to arrive in New York today, and scheduled to reach Washington on Thursday. His meeting with the President is set for Friday morning, and by then, the White House noted. Vance will have returned from the Middle East with his report to the President on his diplomatic soundings in Egypt, Israel, Jordan, Lebanon, Syria and Saudi Arabia.

Only one meeting between Carter and Begin is currently planned. On Friday afternoon Carter is scheduled to fly to Fayetteville, N.C., to attend the Saturday wedding of a nephew.

Begin suggested the talk with Carter when he met with Vance in Jerusalem soom after Vance's arrival there Saturday night. A reply from Carter welcoming the visit was delivered in Jerusalem within a few hours, Sunday morning, White House press secretary Jody Powell told reporters.

U.S. officials said Egyptian President Sadat was consulted about the Begin trip.

Powell said there are bno plans for Sadat or other Middle East leaders to visit Washington.