Despite a dramatic forecast of robust U.S. economic growth by his treasury secretary, President Reagan today failed to assuage the fears of other leaders at this ninth economic summit that continued large budget deficits will jeopardize western economic recovery, officials of several European countries said.

Treasury Secretary Donald T. Regan startled the finance ministers of the other six summit nations Saturday night when he told them at a closed meeting that the U.S. economy may expand by an annual rate of 5 to 6 percent during the current three-month quarter. This would exceed the most optimistic predictions and be nearly double the 3.1 percent first quarter growth rate.

Economic growth of such magnitude would point to a sustained recovery from the severe worldwide recession and could significantly reduce unemployment in the seven summit nations, where 22 million people are now out of work.

Despite this rosy forecast, the heads of state and finance ministers of several other nations were skeptical that U.S. budget deficits would be reduced sufficiently to bring down interest rates and sustain a prolonged recovery, officials of these nations said.

Their objections, voiced in private meetings, indicated far more disagreement on economic policy than has been reflected in public statements by U.S. officials about harmony among the nations: the United States, Canada, Britain, France, West Germany, Italy and Japan.

In briefing reporters after today's sessions, Regan and Secretary of State George P. Shultz maintained the optimistic theme but acknowledged European concern about unemployment, high interest rates and a U.S. budget deficit expected to reach $200 billion in fiscal 1984. Regan said there were "good exchanges" but "no voices raised."

However, French Finance Minister Jacques Delors told reporters that the discussion on interest rates and budget deficits had been marked by "controversy" and "quarrels." He said France pressed its view that the seven countries had to take "a long-term view" and could not depend solely on the signs of an American recovery to resolve world economic problems.

West German sources said Chancellor Helmut Kohl, more than any of the other leaders, emphasized the urgent need to tackle burgeoning U.S. deficits, which Europeans blame for keeping interest rates high.

British Prime Minister Margaret Thatcher told reporters that she defended Reagan's economic policies and sought to blame the problem on the U.S. Congress. "President Reagan and his financial advisers would not argue about fiscal discipline . . . ," she said. "They have, after all, tried very hard in Congress to get the deficit down."

But she also emphasized that "high interest rates are one of the single most important financial things" and that sustaining the recovery would require "keeping deficits down, keeping interest rates down."

The Europeans fear that big U.S. budget deficits will require such extensive government borrowing that interest rates will remain too high to sustain recovery. Kohl reportedly told the others that sustained recovery is so crucial to reduced unemployment that it should be considered a top priority for the security of western society, according to West German officials.

Other sources said Italian caretaker Prime Minister Amintore Fanfani and Gaston Thorn, president of the Commission of the European Communities (the Common Market), also questioned whether the U.S. recovery would be strong enough to ease unemployment in the western world.

Concern about the urgent need to reduce U.S. budget deficits is so widespread that officials from nearly every delegation said their head of government had taken the strongest position in demanding remedies. Thorn was reported to have said that a change is needed "very soon" to keep unemployment from increasing still further in Europe.

Regan acknowledged to reporters that all the others asked: "Could the United States get their interest rates down?" But he argued that there is not necessarily linkage between the big U.S. budget deficits and high interest rates.

He also denied that the Reagan administration had any less of a sense of urgency about bringing interest rates down. But, he added, "We don't necessarily have to have in this first year of recovery interest rates coming down in order to have the recovery."

This is the major disagreement between the United States and the other governments, who believe U.S. interest rates must come down. Concerned that Americans are overstating the current strength of the recovery, their officials say that it will be dissipated if interest rates start rising again if the Reagan administration is seen to be doing nothing to reduce budget deficits.

The seven finance ministers met for the second time today and were reported to be moving toward approval of a study that could lead to a global monetary conference. This issue presumably will be addressed in a general statement to be issued by the heads of government before adjournment of the summit Monday.

At Saturday's dinner meeting of finance ministers, Regan added that the U.S. economic growth in the third quarter of this year might not be quite as strong as in the second quarter but that it would stay relatively buoyant. He said it would be bolstered by the third stage of the administration's income tax cut, scheduled to take effect July 1.

Until Regan spoke, there had been no public or private administration estimate of U.S. growth in the second quarter beyond a general assumption that it would top the first quarter, which was weaker than predicted.

A surge of the dimensions forecast by Regan would help pull the allies out of recession and might alleviate European fears, articulated most clearly by French President Francois Mitterrand, that the recovery will wane before it begins to reduce unemployment significantly.

"That kind of recovery," an Italian source said, "would ease our concerns over a whole range of economic subjects."

But the optimistic U.S. line did not persuade the finance ministers or many of the heads of state that the sharper U.S. recovery projected by Regan would reduce the U.S. budget deficit sufficently to alleviate European concerns about high interest rates.

Regan indicated that the Federal Reserve Board agrees with the administration assessment that the economy is ready to "take off." It was learned that Regan spent an hour discussing the economic outlook with Federal Reserve Board Chairman Paul A. Volcker before coming here Friday.

Volcker's status after his term as chairman expires in August is uncertain. But he is highly regarded in Europe and Regan did not hesitate to invoke his name to give added weight to what the administration considers a significant development.

An economic surge of the magnitude predicted by Regan probably would have major domestic political benefit for the president, whose economic program failed to produce the early results he promised.

While summit participants were arguing among themselves on the major issues of budget deficits, interest rates and nuclear arms control, their aides kept up a valiant show of unity on a day when public appearances of even a ceremonial nature were limited.

White House deputy chief of staff Michael K. Deaver, a chief orchestrator of the summit, was particularly ebullient, saying, "They're all getting along fine."

But French officials were particularly acerbic in criticizing proceedings so far, reflecting their country's currently severe economic problems and the fact that so much of the first 24 hours of the economic summit were consumed by a long, difficult debate over arms control policy.

U.S. officials insisted that considerable time was devoted to economic questions today and added that Mitterrand himself agreed, if reluctantly, to the discussion and drafting of a declaration on arms control.