The western world's top leaders are heading for their 13th annual economic summit in Venice worried about economic growth, their mood markedly different from the upbeat expectations that preceded the 1986 Tokyo summit.

At best, the seven heads of government -- most of whom have suffered declining popularity or face national election contests within the next several months -- say they will offer no new initiatives, merely an earnest effort to translate older agreements into action.

President Reagan, moving toward the end of his final term and damaged by the Iran-contra scandal, may also find American leadership diminished by the fact that the United States has become a debtor nation, while other powers, notably Japan and West Germany, are enjoying relative economic success and surpluses.

In this situation, all delegations have been careful to suggest that more important results may come out of noneconomic discussions in Venice on such topics as the war in the Persian Gulf, East-West relationships or the AIDS epidemic.

"The best thing about the Venice summit will be Venice itself," said one of the Canadian officials preparing for the three-day meeting, which begins Monday. It will be attended by heads of government from the United States, West Germany, Japan, Britain, France, Canada, and Italy as well as representatives of the European Community.

The series of summit meetings was launched under the stewardship of former French president Valery Giscard d'Estaing and former West German chancellor Helmut Schmidt in Rambouillet, France, in 1975.

To a certain degree, this summit, at least on the economic side, will sound like a replay of recent meetings of the International Monetary Fund or the Organization of Economic Cooperation and Development in Paris, with the leaders endorsing agreements drafted earlier by their finance ministers.

As Treasury Secretary James A. Baker III put it this week: "You shouldn't expect to see {new policy measures} every time there's a multilateral gathering. The question is implementation, so we will go to the summit with the view that we have {already} agreed upon what needs to be done."

President Reagan said before leaving Washington for Venice: "I'll ask the leaders of the other industrial nations to stimulate their economies. We want them to buy more goods, not only from America, but from . . . the world, so they can help us make prosperity worldwide."

That's been the exact pitch, for the past two years, from the American side, with only limited results. As Alan Greenspan, the new chairman-designate of the Federal Reserve Board, has emphasized, such appeals are heeded only to the extent that they match domestic priorities. Japan and, most notably, West Germany move slowly on domestic expansion, hesitant to renew inflation.

Equally, the demand by West Germany and Japan that the United States get its own house in order by slashing its federal budget deficit has a limited impact.

"Whatever Reagan's good intention on the budget, it's not a parliamentary system in the U.S.", said a European Community spokesman. "Reagan still has to deal with Congress."

By being beholden to other nations -- especially Japan -- to finance its deficits, the United States now has fewer economic resources of its own to stimulate the world economy and less political influence in setting the economic agenda.

But Japan comes to the summit only days after outlining a $43 billion fiscal expansion plan that it initially promised in early international meetings.

"This is Japan's largest public works expenditure in 10 years," said Koji Watanabe of the Japanese Ministry of Foreign Affairs. The unspoken hope is that the Japanese package, which the others agree this time involves "real money," will put similar pressure on the Germans.

With the new fiscal package and an additional $20 billion pledged for aid to Third World countries, Japanese officials predicted that the usual criticism of their failures to open markets will be minimized in Venice.

The Germans, meanwhile, said they will repeat their earlier commitment to cut taxes, but Kohl will carefully avoid making new promises to expand the economy.

"The problem with the Japanese is that they make acceptable promises, but you have to press them to make good on them," complained a senior U.S. official.

"You don't have that problem with the Germans: they do just what they say they will do. The problem with the Germans is that you can't get them to move enough: they are too hung up in their psychological fix about inflation."

As the leaders meet, the global economic outlook is somewhat shaky. Undersecretary of State Allen Wallis, the summit preparer for Reagan, said last week, "We've got problems . . . . The growth in the summit countries is not as strong as it could be and ought to be, and furthermore, it seems to be weakening. And unemployment, especially in Europe, remains very troublesome."

Uncertain prospects for economic growth and recent volatility in the exchange markets were complicated further by the dramatic decision by Federal Reserve Board Chairman Paul A. Volcker to retire in August.

"Somehow, the economic world won't be the same any more," said Dietrich von Kyaw, economics minister of the West German Embassy in Washington. "Paul Volcker not only broke the back of inflation, but in the early years, he also contained the debt crisis."

Although Reagan's quick choice of Greenspan, another fiscal conservative, to succeed Volcker has been widely applauded, the upcoming shift adds one more element to a picture of uncertainty that contrasts sharply with the optimism that preceded the Tokyo summit.

Then, the expectation was that the decline in the dollar, and lower interest rates and oil prices promised a noninflationary revival of the global economy that would reduce the huge U.S. trade deficit, as well as ease worries about the Third World debt that overhangs the banking system.

That outlook led to firm declarations of unity and to acceptance of an ambitious plan by Baker to work out a new technical process to support economic coordination, built on certain economic indicators that are supposed to measure how well policy coordination is going.

But some funny things happened on the road from Tokyo to Venice. The oil price decline did reduce the inflation indexes, but lower oil prices also had a negative impact on economic activity in the producing regions, including the southwestern United States.

In addition, the decline of the dollar has had little beneficial effect on reducing the U.S. trade deficit. In fact, it increased, with the result that the United States emerged as the world's largest debtor nation while Japan has become the biggest creditor. The appreciation of the yen and the West German mark, meanwhile, began to have a restraining influence on economic growth in Japan and Germany.

In part because of the loss of oil revenues, the Third World debt situation continued to be worrisome, especially because commercial banks became hesitant to extend new loans they had promised under the debt initiative launched by Baker in October 1985.

Postponement of interest payments by Brazil and other important debtor nations, and the recent decision by large American banks to increase their reserves against the possibility that some of the principal will never be paid off have again made the debt crisis a priority.

For all of these reasons, the cooperative mood in Tokyo turned into bickering among the three major powers. Quickly, the once harmonious efforts to manage the currency system, which had started with an agreement reached at New York City's Plaza hotel in September 1985, disintegrated into public disputes over exchange rate levels, especially between the United States and West Germany.

As if to teach West Germany a lesson, Baker and Japanese Finance Minister Kiichi Miyazawa struck a bilateral deal in October 1986 the first step toward stabilizing the yen-dollar exchange rate, along with a commitment by Japan to expand its fiscal policy at home.

Meanwhile, the disappointing trade results -- a global U.S. deficit that zoomed from $148.5 billion in 1985 to $169.8 billion in 1986 -- strengthened the conviction among congressional Democrats that the time was ripe for a legislative response incorporating punitive protectionist devices. The Reagan administration felt constrained to respond to a charge that Japan had been dumping semiconductors in violation of a specific agreement by imposing $300 million worth of sanctions on Japanese exports of electronics products. These sanctions are still in effect, although Japan had been hoping that they might be lifted or eased by this time. "The very notion of sanctions to us is obnoxious," said Watanabe. "It's a clear violation of GATT {international trade} rules." The imposition of sanctions by the United States against its number two trading partner was symbolic of the disintegration of the unity following the Tokyo meeting. Beyond their concern about the broad threat to the trading system, Europeans fear that the result of bilateral pressures by the United States against Japan will be even more Japanese goods spilling over into Europe.