A 34-nation conference here last week on President Reagan's "campaign for democracy" showed that the United States cannot automatically count on other democracies to share its priorities for conducting a global anti-communist offensive.

Last June in London, the president projected a long-term drive to challenge communism in its own sphere, ultimately dumping "Marxism-Leninism on the ash heap of history . . . ."

In three days of discussions, however, participants in a Conference on Free Elections demonstrated far more interest in strengthening and broadening democracy in their own areas, in Latin America especially, and elsewhere in the West and in the Third World.

There is nothing inconsistent about these two objectives, American officials said yesterday at the end of the conference, sponsored by the State Department and the American Enterprise Institute.

A related Conference on Democratization of Communist Countries was held last month as part of the preparatory work for the Reagan-initiated campaign.

Both conferences, and studies to follow, are described as forums for an "exchange of ideas" about how to enhance the spread of democracy.

In the mid-October meeting, Secretary of State George P. Shultz disavowed any intent "to foment violent unrest or to undermine communist regimes." At the same time, Shultz and other U.S. officials said "we must aid" those who "struggle for freedom."

When last week's conference opened, the emphasis was on the positive aspects of democracy rather than anti-communism per se. Shultz said, "We are not here to challenge other countries, but to extend an offer to share our experience and our expertise in making freedom work."

The Soviet Union has scoffed at these American distinctions as transparent attempts to veil what Soviet President Leonid I. Brezhnev has denounced as portions of an overall American policy of "adventurism, rudeness and undisguised egoism."

The basic Reagan administration response, first set forth by the president in June, is that Brezhnev himself "repeatedly has stressed that the competition of ideas and systems . . . is entirely consistent with relaxation of tensions and peace." It is the administration's position, therefore, that the United States is only responding belatedly to a challenge that the Soviet Union has been posing for decades.

Unlike the Soviet Union, however, the United States by no means controls the ideological struggle on its side of the East-West divide.

The diversity inherent in the democratic process was openly on display in the latest conference, demonstrating the complexity of even defining the goals of the intended campaign.

In welcoming the delegates, Reagan described them as "representatives of thriving democracies of many nations." In fact, they covered a spectrum that included such countries as Argentina and Turkey, which are under military rule. One speaker, Italian Prime Minister Giovanni Spadolini, after deploring the repression of human rights in communist Poland, next cited in dismay "the trauma in Argentina."

While some participants wanted to hammer out the criteria for democracy, others opposed that.

Democracy's strength, said Costa Rican President Luis Alberto Monge, is the absence of "universal formulas with which to confront the economic and social problems of any given society." This, he said, "is its essential difference from totalitarian philosophies such as nazism, fascism and communism, which expand by requiring that experiences, methods, and institutions be imitated, copied and transplanted."

American speakers extolled free elections as the touchstone of democracy, but not all participants concurred on even that criterion as absolute.

Jeane J. Kirkpatrick, U.S. ambassador to the United Nations, said, "It is very clear that legitimate government . . . is government whose chief decision-makers are chosen through democratic elections." The critical test of the equity of the election process, she said, is that leaders "run the risk of defeat," and democratic leaders therefore must "risk power for the sake of freedom."

Mexico's Edmundo Hernandez Vela said the conference should ask "Why necessarily elections?" and "What does freedom mean?"

A. J. Wilson of Sri Lanka said that, without "responsible political leadership" and "an informed electorate that cannot be easily misled," electoral "contests" can be converted into "auctioneering games."

Homogeneous societies in which democracy is deeply imbedded, said Vernon Bogdanor of Oxford University, need to recognize a special dilemma of Third World countries. Where there are deep divisions of language, religion, race or region, he said, "the defeat of one party by another will seem to the losing side not as a swing of the pendulum, but rather as a defeat for its whole way of life. . . ."

Conference moderator Austin Ranney of the American Enterprise Institute said it was agreed in advance that there would be "no formal resolutions." Specific programs to encourage free elections and constitutional government are to be developed in further studies.