President Carter has backed away from his effort to persuade West Germany and Japan to expand their economies faster, settling instead for a less ambitious "commitment" to take whatever steps are necessary to achieve previously announced growth targets.

This was announced today by Treasury Secretary W. Michael Blumenthal at the conclusion of the first session of a two-day economic meeting of seven heads of government here.

Blumenthal said, nevertheless, that all the leaders had agreed that world economic recovery is not proceeding fast enough, that "confidence is lagging" and that there was complete accord on the need "to reject protectionism" as a solution to problems.

Before coming to the summit, Carter had stressed the need for faster economic growth in both West Germany and Japan as a way of spreading strength through the rest of the Western world. Such expansion, according to this theory, would have helped the smaller countries cut their deficits through sending more exports to the United States, West Germany and Japan.

The commitment made today, Blumenthal said, would insure a smaller rate of growth that would still reduce worldwide unemployment but would not produce new inflation, which often results from efforts to stimulate a sluggish economy.

After a breakfast meeting this morning before the first summit session, Carter joined West German Chancellor Helmut Schmidt in striving to put a better face on the disputes between them.

Carter told a reporter that "there are no remaining differences between us." Schmidt said that the breakfast talk "had been good, if not to say excellent." He added that he and Carter had "got over some specifies" at the dinner given last night by Prime Minister James Callaghan.

"The meeting was very direct," said Carter's national security adviser, Zbigniew Brzezinski. "They are both sharp and quick and they know their stuff. They were two people trying to understand each other. Both have a healthy respect for one another."

Carter's decision Thursday to allow renewed shipments of enriched uranium to West Germany and other specified countries solved one major U.S.-West German problem. The U.S. withdrawal of public pressure on West Germany to accelerate economic activity may defuse another Privately, however, U.S. officials think that the Germans will have to put more impetus into their economy to achieve their stated growth goal.

Officials on both sides were eager to get the Carter-Schmidt quarrel patched up. "As politicians," said one U.S. aide, "they really both have a lot in common."

Blumenthal described the first session of the seven leaders as "a very good, cooperative, friendly and frank framework for discussion of other items" in addition to economic expansion. These included so-called "north-south" problems (those dealing with rich nation-poor nation relations), lendable resources of the international institutions, specific trade problems and energy.

Blumenthal claimed that the international agreement to make good on national economic targets, to be presented in a communique, Sunday, is one of the "new initiatives" Carter had promised. He said it implies that if the targets individual nations - including the United States - set are not met, they would have to take expansionary action to fulfill them.

The afternoon session produced only two tidbits of news. One was Blumenthal's report that all of the leaders "welcomed" Carter's emphasis on human rights, as Carter - at his own initiative - explained it to them briefly. Another was the announcement by Jody Powell, Carter's press secretary, that Britain had been added to the list of nations authorized to receive enriched uranium.

The summit meeting - third in a series after sessions at Rambouillet, France, and Puerto Rico - got under way on schedule this morning in the state dining room in the British prime minister's residence at 10 Downing Street.

Besides Carter, Schmidt and Callaghan, the host, French President Valery Giscard d'Estaing, Canadian Prime Minister Pierre Trudeau, Italian Prime Minister Giulio Andreotti and Japanese Prime Minister Takeo Fukuda attended. Each had two seats for aides, Carter's being Blumenthal and Secretary of State Cyrus Vance.

Common Market Commission President Roy Jenkins, who had been invited to attend, was not at the first session, although it dealt with world economic problems.

Blumenthal refused to say whether the United States is "satisfied" with the announced growth targets of other nations - 5 per cent for West Germany and 6.7 per cent for Japan. But officials said privately that the United States had concluded that little could be gained from pushing the issue further.

"There was no attempt to change targets or negotiate," Blumenthal said, "but there was general agreement that the targets that countries had previously stated would be met, and that they would do what is necessary to meet them."

He quoted Carter as "certain" and confident" that the U.S. target of 5.8 to 6 percent in real growth between the last quarter of 1976 and the last quarter of 1977 would be achieved.

In recent weeks Carter's economic advisrs have stressed the lower end of the range as more feasible. Two weeks ago, the U.S. government lowered its growth estimate for calendar 1977 from 5.4 to 4.9 per cent after the $50 tax rebate and other budget changes cut the fiscal 1977 deficit by $19 billion.

Blumenthal said there was "some mention" during the summit session of the withdrawal of the rebate, but that there had been "no criticism" of it. Privately, other nations have been criticial of the rebate withdrawal, in view of earlier U.S. pressure on West Germany and Japan to expand their economies.

Carter's defense, according to Blumenthal, was that the U.S. economy is responding nicely to prospects of increasing business investment. After a first-quarter gain of 5.2 per cent in the gross national product, U.S. economists expect a second-quarter increase of more than 7 per cent. Carter also cited the decline in the unemployment rate from 7.3 to 7.0 per cent in April, announced the day before the summit meeting started. He said this assured a drop below that level - which had been the target for end of 1977.

Blumenthal's passing references to protectionism - which are to be dealt with more fully at the Sunday morning session - aroused special interest in two ways. First, there was an expected, strong rejection of the use of protectionist policies.

But Blumenthal also carefully set out that Carter's liberal stand on trade, as reflected in his past decisions on shoes and sugar "and on future decisions that he has to make, (means) he certainly will be very careful in balancing the domestic considerations against international obligations."

This is an oblique reference to the continuing discussions here between special trade representative Robert Strauss and the Japanese on an informal agreement to limit the sale of color TV sets to the United States.