The United States formally pulled out of UNESCO today, plunging an institution that had aspired to become the world's leading think tank into the most serious political and financial crisis in its history.

Demoralized by a series of resignations of senior staff members and attacks on its professional expertise, the U.N. Educational, Scientific and Cultural Organization now faces the immediate task of cutting back its regular $260 million annual budget by 25 percent virtually overnight. Public interest in its activities, already waning, is likely to be reduced still further without the participation of its wealthiest and most powerful member state.

Both Britain and Singapore have given notice that they, too, will leave the 161-member organization at the end of next year unless major changes are introduced. Similar, if less explicit, threats have been made by West Germany, Japan and Belgium, which have echoed U.S. complaints that UNESCO is badly managed and too politicized.

Founded at the end of World War II with the aim of promoting peace through "equal education for all, the unrestricted pursuit of objective truth, and the free exchange of ideas and knowledge," UNESCO is widely seen today as the weakest and most controversial link in the United Nations system. The way it tackles its present crisis is bound to have an important impact on the future of multinational diplomacy as an instrument of international cooperation.

Interviews with diplomats and officials at UNESCO headquarters in Paris suggest, however, that there is a wide range of opinions about the long-term practical effects of U.S. withdrawal.

Supporters of the Reagan administration's action argue that the organization will be forced to speed up the implementation of changes to prevent further defections and to entice the United States back. The U.S. decision is seen as a way of keeping up the pressure on UNESCO's beleaguered director general, Amadou Mahtar Mbow, to pay more attention to western concerns.

An encouraging precedent, according to this view, was provided by the efforts made by another U.N. body, the International Labor Organization, to reform itself following the U.S. withdrawal in the mid-1970s. The staff was immediately cut and more attention was given to western complaints about the violation of union rights in Soviet Bloc countries, with the result that the United States is now back in the ILO, but Poland has withdrawn after being criticized for its suppression of Solidarity.

"It would be counterproductive for UNESCO to become more radical if it wants to get universal support," commented departing U.S. Ambassador Jean Gerard in an interview.

Gerard became involved in a dispute with Mbow as she left, news agencies reported. Mbow had said in a French television interview Saturday that the United States was withdrawing from the agency for political reasons and that Gerard was "unaware of what does on" in UNESCO.

Gerard countered in a written statement Monday that Mbow had failed "in his duties of reserve and impartiality," The Associated Press reported from Paris.

Critics of the U.S. withdrawal from UNESCO, who include some western delegates as well as the vast majority of Third World representatives, take the opposite view from Gerard's. They maintain that Mbow and his backers, having made a serious but fruitless attempt to accommodate the United States over the past year, will now lose interest in reform and become even more susceptible to Soviet Bloc blandishments.

"Third World countries see the American action as a shot across the bow of the entire United Nations system. They believe that the U.S. was determined to make a political point by withdrawing from UNESCO in any event -- no matter how much reform was introduced -- and I think they are probably right," commented one western ambassador who asked not to be named.

A third view, suggested by a disgruntled member of the UNESCO international secretariat opposed to Mbow's leadership, is that U.S. withdrawal will make very little difference either way.

"As long as Mbow remains director general, there will be no serious reform. He is opposed to all change as he thinks that it implies a criticism of the way he has been running the organization over the past 10 years -- as indeed it does. He behaves like the typical dictator of a small African state," he complained.

Described as charming, cunning and authoritarian, the former Senegalese school teacher is a symbol of the sharp shift in the balance of power that has occurred at UNESCO and other U.N. agencies over the past four decades. He owed his election in 1974 to the wave of decolonialization that ensured African, Arab, and Asian countries a majority in the U.N. system and diluted respect for western liberal ideas. UNESCO's membership has expanded more than fivefold since 1945.

Mbow was reelected to a second seven-year term in 1980 with both western and Soviet Bloc support.

In a recent interview in his spacious office, which is cluttered with piles of UNESCO documents, African sculptures and a personal computer, Mbow presented himself as the conscientious executor of the wishes of member states. He pointed out that the United States had given its consent to many of the programs now criticized by the Reagan administration because of their alleged political bias.

Mbow's attempts to depict Washington's move as motivated by frustration with the loss of political power rather than by real concern for the way UNESCO is run have met with some success in Third World circles. A commentary in this week's edition of Jeune Afrique, a Paris-based publication widely circulated in Africa, accused the United States of instigating a press campaign against Mbow that smacked of both racism and arrogance.

The magazine approvingly quoted Mbow as telling Ambassador Gerard at a celebrated meeting in June 1983 before the United States gave notice of its intention to withdraw from UNESCO: "Remember, madam, you are not speaking to a Negro from Mississippi." The same incident is cited by many western diplomats as evidence of what they see as the director general's paranoia and refusal to accept legitimate criticism.

In a statement earlier this month, confirming the U.S. intention to withdraw from UNESCO at the end of this year, the State Department accused the organization of "an endemic hostility toward the institutions of a free society" and lack of concern with "individual human rights."

As an example of mismanagement, it said 80 percent of UNESCO expenditures occurred in Paris rather than in the field. Mbow denied this in the television interview but did not offer another figure. The agency has more than 3,300 employes.

Mbow said in a recent interview that the 82 U.S. citizens who hold professional positions in the agency are "part of the international staff" and would not be affected by the U.S. withdrawal.

Although most western delegates share the U.S. concerns about UNESCO, the Reagan administration's tactics have come in for some criticism.

The sharpest attack has come from the former Labor Party prime minister of Australia, Gough Whitlam, now his country's ambassador to UNESCO. He has accused Gerard of whipping up a press campaign in Britain to pressure the Thatcher government into following the U.S. lead.

According to Whitlam, Gerard left a meeting of UNESCO's executive board meeting in Paris last month to lobby British legislators and journalists in London.

A spate of articles appeared in the British press arguing in favor of British withdrawal following Gerard's visit.

Gerard dismissed Whitlam's accusations, saying that she had a "long-standing invitation" to visit Britain.

She added that British Prime Minister Margaret Thatcher was "perfectly capable of pursuing an independent policy toward UNESCO" without being influenced by the United States.

Most western delegates concede that last year's U.S. decision to give notice of its intention to withdraw from UNESCO jolted the organization into making some changes aimed at streamlining its activities and avoiding duplication of programs.

"In retrospect, there is no question that the threat of U.S. withdrawal provided an impetus to reform," said Canadian Ambassador Ian Christie-Clark. "At the time, I had the impression that it might be regarded as blackmail by Third World countries and backfire. It didn't."

The Canadian delegate made clear, however, that he believed the departure of founding members of UNESCO could be counterproductive.

"The U.S. criticisms of UNESCO are shared by like-minded countries. But there is a question of how far and how fast you can go. We have achieved a surprising amount over the past year," he said.

UNESCO's reforms have been described as "insufficient" by the Reagan administration.

U.S. officials depict the director general's action in setting up five working groups to study possible changes in the way UNESCO is run as largely cosmetic.

Defending the U.S. withdrawal, Gerard said: "People stop listening if you criticize without doing anything. We believe in free world values and have been willing to stand up and say so . . . . We have shown that we take UNESCO seriously."