After observing Yom Kippur, the Jewish Day of Atonement, with his compatriots, Prime Minister Shimon Peres left here tonight for the United States on a mission geared toward ensuring traditional U.S. financial support for Israel's crippled economy.

What form that support will take is uncertain and the subject of endless speculation here. But there is widespread agreement that the Israeli economy is continuing to deteriorate, and that reviving the economy will require additional U.S. assistance.

"It does come down to dollars," Nimrod Novick, chief political adviser to Peres, said this week. He declined to discuss the specific measures that Peres intends to raise.

For Peres, who is due to arrive in New York Sunday morning, the trip to the United States is his first as Israel's prime minister. He assumed the post less than a month ago as the head of a national unity government dominated by Peres' Labor Party and the rival Likud bloc.

Peres has an extraordinarily crowded schedule during his seven-day trip. It includes a meeting Tuesday at the White House with President Reagan, five separate meetings with Secretary of State George P. Shultz and sessions with Vice President Bush, Defense Secretary Caspar W. Weinberger and U.S. Ambassador to the United Nations Jeane J. Kirkpatrick.

Peres will also see Democratic presidential nominee Walter F. Mondale, a visit cited by the prime minister's aides as proof of the "bipartisan" nature of the visit, as well as former secretaries of state Cyrus R. Vance and Henry A. Kissinger, AFL-CIO President Lane Kirkland and dozens of American Jewish leaders.

Tagging along at Peres' side at most if not all of these meetings will be a visible reminder of the uneasy alliance that produced the national unity government: Foreign Minister and "alternate" prime minister Yitzhak Shamir, the leader of the Likud bloc.

With these two men and their parties deeply divided over the future of the Israeli-occupied West Bank and Gaza Strip, it is doubtful that the three days of talks in Washington will produce much momentum toward reviving the overall Middle East peace process.

There is far more agreement within the Israeli government on the objective of an Israeli troop withdrawal from Lebanon, and Lebanon is likely to be on the agenda of the Washington talks.

The Israeli economy, however, is expected to dominate the Washington meetings. The economy -- with its annual inflation rate accelerating beyond 400 percent, a gaping balance of payments deficit and huge foreign debt, dwindling foreign currency reserves and stagnant productivity -- is the primary reason for Peres' early visit to the U.S. capital.

Peres and his aides publicly have ruled out asking the Reagan administration for an immediate emergency infusion of U.S. funds. The prime minister, his aides say, will not be returning to Israel in a week "with a check in his pocket."

During the past two weeks, Peres has signaled the tone he intends to convey in Washington, portraying himself as the new leader of a beleaguered small country that is determined to reverse its economic decline, at whatever sacrifice.

"I'm not going like a beggar," he said in a recent radio interview. "I'm not going to ask for another $100 or $200 million -- that would be a mistake. I'm going to discuss a more general, more basic view regarding the future of the Israeli economy, and the United States is very interested in Israel's economic situation. It wants its most important friend in the Middle East to be strong economically."

In the past week, the Israeli press has engaged in extensive speculation about just what the prime minister will ask of the U.S. administration. The reported options include major increases in the levels of military and economic assistance beginning in the next fiscal year, a long-term loan to be used to spur Israel's high-technology industries and the creation of an "emergency fund" Israel could draw on if its foreign-currency reserves continue to decline.

Peres has stressed the need for a restructuring of U.S. aid to direct the assistance more toward long-term economic growth. But Israel's most immediate need appears to be some kind of U.S. backing to shore up its battered international credit rating, allowing the government to continue to raise money from private sources and keep the economy afloat.

In ruling out a request for an immediate cash "handout," the Peres government has given up little. Congress is about to adjourn for the year, leaving no prospect of an emergency appropriation before January. Moreover, there is doubt that the austerity measures the Peres government has imposed so far will be viewed in Washington as satisfactory evidence that Israel is serious about reforming its profligate ways. The Reagan administration has always conditioned U.S. aid on "meaningful" reforms in the Israeli economic system.

Until recently, Israeli officials spoke of seeking a stopgap grant of $700 million to $1 billion, in addition to the $2.6 billion in regular military and economic assistance that Israel will receive this fiscal year. But two weeks ago, U.S. Ambassador Samuel W. Lewis delivered what was described as a strong reiteration of the administration's expectations to Finance Minister Yitzhak Modai, who later told a group of Israeli businessmen, "Only we can save ourselves." It was then that Peres began speaking publicly about the importance of long-term growth and saying that he did not intend to go to Washington as a "beggar."

What the Peres government has done so far is agree to cut the government budget by $1 billion during the next year. A number of economists in Israel, however, maintain that a $1 billion budget cut is insufficient given the country's precarious economic health. The budget needs an immediate cut of $1.5 billion to $2 billion, they say. Peres has said that $1 billion is all the country can bear for the moment.

The government also devalued the currency by 9 percent and slashed subsidies on basic commodities such as dairy products, bread and fuel. The level of government subsidies, however, remains high. The immediate effect of the subsidy cuts will be to push Israel's inflation rate to even more alarming heights. According to some calculations, the monthly rise in the consumer price index is approaching 1,000 percent if compounded on an annual basis.

In moves this week before Peres' departure, the government also imposed a total import ban on 50 "luxury" consumer items such as automobiles and television sets. The Likud government's policy of encouraging spending on these items contributed heavily to Israel's balance of payments and foreign debt problems. The new ban, however, is to last for only six months.

According to Peres and his aides, these steps are only part of an overall plan to put the economy back on course. The key to that plan, they say, is a "package deal" among government, business and labor to freeze or greatly restrain wage and price increases.