Representatives of the United States and Israel sat down last night to negotiate their own diplomatic arrangements to back up the Egyptian-Israeli peace treaty, which is to be signed Monday afternoon on the front lawn of the White House.

Secretary of State Cyrus R. Vance and Israeli Foreign Minister Moshe Dayan, aided by their delegations, went to work at the State Department on a "memorandum of agreement" on political and military relations flowing from the U.S.-sponsored Mideast pact.

A key question is the extent to which the United States will give Israel a veto power over American dealings with Palestinians, whose future is central to the comprehensive peace in the Mideast region that President Carter has been seeking in his two years in office.

In September 1975, Secretary of State Henry A. Kissinger, in a similar memo with Israel in connection with the Sinai disengagement pact; agreed that the United States would neither recognize nor negotiate with the Palestine Liberation Organization as long as the PLO did not recognize Israel's right to exist.

In the current negotiations, Israel is reported to be seeking tight assurances from the United States on Palestinian contacts, diplomatic coordination at the United Nations and else-where, and U.S. actions in case the peace treaty should be violated by Egypt. Sources said the United States is seeking to retain flexibility for future action, while meeting Israel's desire for clear indications of continued U.S. backing.

Sources familiar with the draft text of the U.S. version of the memo said it gives extensive commitments to consult and coordinate with Israel on political and military contingencies, and to favorably consider Israeli requests for armaments.

"We in Israel think that the United States, more than just a mediator, is a partner and we would like the United States to have a role or some responsibility in the implementation" of the treaty between Egypt and Israel, Dayan said after a two-hour meeting with Vance and aides on both sides. Dayan said the negotiations will continue early today.

Administration officials said Carter has reaffirmed that the United States continues to be bound by the 1975 commitment to Israel regarding contacts with the PLO. At the same time, the next phase of Middle East negotiations clearly will require the United States to accelerate its contacts with

Palestinians who are in positions of leadership, the officials said. Many ways have been examined within the administration for addressing the Palestinian issue without breaching the 1975 memo to Israel.

State Department spokesman Hodding Carter said that, unlike the 1975 Kissinger memo that it will supersede, the new document will not be a secret but will be made public without delay. Nothing under discussion "is in the nature of treaty commitments" by the United States, and nothing in the finished memo will require congressional action, Carter said.

Israel proposed written guarantees from the United States in connection with an Egyptian-Israeli peace treaty many months ago, according to administration officials. Draft memos were exchanged between American and Israeli officials during Carter's recent negotiating trip to the Middle East, and a further set has been exchanged since then, officials said.

Egypt has said it is not interested in such written assurances, according to officials.

In addition to the "memorandum of agreement," other outstanding matters to be resolved in the next several days are:

A final, detailed timetable, to be attached to the treaty as an annex, for Israeli withdrawal from the Sinai. Israeli Defense Minister Ezer Weizman is expected here today to negotiate with Egyptian Defense Minister Kamal Hassan Ali. The remaining disagreement centers on when Israel will stop pumping oil and withdraw from the Sinai oil fields it is giving back to Egypt.

Details of U.S. guarantees to make up any deficit in Israel's oil supply over the next 15 years. Legal advisers of the State Department and the Israeli foreign ministry are a work on this issue.

Egyptian President Anwar Sadat and Israeli Prime Minister Menachem Begin, each of whom will be accompanied by his wife and a high-level official delegation, are to arrive Sunday afternoon at Andrews Air Force Base.

The White House said the treaty-signing ceremony, scheduled for 2 p.m. Monday on the White House North Lawn, facing Pennsylvania Avenue, will be televised live to the Middle East.

The North Lawn, a rarely used site for ceremonies in recent years, was chosen because a large tent has been erected on the South Lawn to seat 1,300 people for a state dinner Monday. Each of the three nations will provide some of the entertainment, officials said.

An "ecumenical prayer service" is scheduled for shortly before the state dinner. Officials said a plan to hold the service at the Washington Cathedral had been abandoned due to an Israeli objection, and that the most likely site is now the Lincoln Memorial.