The United States scored its most decisive U.N. victory in years today when the General Assembly rejected a Cuban move to hold a full-scale debate on whether Puerto Rico should have independence. The vote was 70 to 30, with 43 abstentions.

This rare American diplomatic triumph was produced by an intense global lobbying campaign -- unprecedented since the battles over Chinese representation in the early 1970s -- that involved Secretary of State George P. Shultz, U.S. ambassadors around the world and most of the American delegates to the United Nations.

"They truly pulled out all the stops," said one African ambassador. He said Shultz had called his president personally to appeal for support and the president in turn had phoned him with instructions to vote with the United States.

As a result of these efforts, the only nations joining the Soviet Bloc and its traditional allies in voting for the Cuban proposal to inscribe "the question of Puerto Rico" on the Assembly's agenda were Albania, Argentina, Ghana and Venezuela.

The U.S. victory here came on the same day that the United States and Israel were dealt a diplomatic setback by another U.N. body, the Vienna-based International Atomic Energy Agency. The 110-member agency, meeting in Vienna, suspended Israel's credentials by a 41-to-39 vote, prompting a walkout by U.S. and British delegates and an American denunciation of the move as "unacceptable."

In the vote here on the issue of Puerto Rico, many nations dependent on American aid that usually abstain in East-West confrontations--such as Pakistan, Bangladesh, Panama and Senegal--voted Washington's way. Even those which habitually vote against American interests despite the bilateral support they receive--such as Tanzania, Guyana, Zimbabwe and Mali--abstained on this occasion.

American officials denied charges by lobbyists for Puerto Rican independence that threats were made to obtain votes. But the American deputy representative, Kenneth Adelman, the field commander of the U.N. lobbying effort, conceded that his troops had made it quite clear to nations considering an abstention that such a vote "would be unfavorably met in bilateral relations and on Capitol Hill."

American Ambassador Jeane Kirkpatrick dismissed suggestions that the intensity of the drive was diplomatic overkill, insisting that "this issue is very, very important; it matters a lot to us," because the Cuban initiative was more than a drive to embarrass Washington or thwart American policy, it was a direct attack on the United States.

A U.N. debate on Puerto Rico, said a fact sheet distributed by the U.S. delegation, "would represent interference in the internal affairs of the United States, a violation of our sovereignty and an attempt to intervene in the political processes of Puerto Rico. . . We very much hope that you will vote against inscription, and not merely abstain."

Kirkpatrick maintained that the United Nations has no jurisdiction over Puerto Rico, as it does over non-self-governing territories, because the island commonwealth has been fully self-governing since 1952, and this was recognized in an Assembly resolution adopted unanimously the following fall.

"Our case is legally, historically, politically and morally unambiguous," she said.

But since 1953, the composition of the United Nations has changed drastically, and now many of the ex-colonies that form its majority hold to the principle that the act of self-determination must lead inexorably to independence.

Over American objections, Cuba began raising the Puerto Rican issue again in the United Nations's decolonization committee. In August 1981, that body called for the subject to be debated by the Assembly this fall, a stage that would have provided advocates of Puerto Rican independence with the international legitimacy they are seeking to increase the popularity of their cause.

Statistics presented by the United States show that pro-independence candidates have won less than one-tenth of the popular vote in Puerto Rican elections over the past two decades, and opinion polls show the same trends.

The mainstream debate on the island is between statehood and continuing commonwealth status. But the economic advantages of both have been called into question by the Reagan administration proposal for a Caribbean Basin Development Plan, which would give neighboring countries the chance to attract capital and to market products in competition with Puerto Rico.

The Cubans did not seek to challenge the statistics. Their ambassador, Raul Roa, argued instead that Puerto Rico is not truly self-governing under U.N. definitions, and that statements to the decolonization committee by leading Puerto Rican citizens "prove unequivocably the dissatisfaction of the people with their present political status."

Hernan Padilla, the mayor of San Juan and a member of the U.S. delegation, spoke for the United States and said Washington had promised to abide by the wishes of the Puerto Rican people on their ultimate status. But he said there "is a consensus that a change will come through our own mechanisms," rather than those of the United Nations.

Padilla said the Cuban initiative offered only one possible outcome, independence, but "we don't want others to close options for us."

The IAEA vote in Vienna climaxed a campaign started after the Israeli bombing of an Iraqi nuclear reactor in 1981. An attempt to expel Israel totally from the agency fell four votes short of the necessary two-thirds majority.

The action taken instead, suspending Israel's credentials for this year's annual IAEA conference, is largely symbolic, since it came on the conference's last day. But State Department officials, citing resolutions passed by Congress last spring calling for suspension of American participation in any U.N. agency that curtails Israel's representation, said the United States would have to reassess its role in IAEA, which includes payment of a quarter of the agency's annual budget of more than $100 million.