The United States, seeking to turn back a rising tide of Latin American bitterness over U.S. policy in the Falkland Islands crisis, appealed yesterday to hemispheric governments to support United Nations peacemaking efforts and avoid actions that might exacerbate the fighting between Britain and Argentina.

"We must strive to resolve the conflict, not seek to widen it," Secretary of State Alexander M. Haig Jr. last night told a special meeting here of foreign ministers of the Organization of American States.

Haig, who canceled a speechmaking trip to Pittsburgh to head the U.S. delegation at the meeting called by Argentina, made his appeal after listening in stony silence to some of the most virulently anti-American rhetoric ever heard in the OAS. His speech was greeted with only scattered and perfunctory applause.

That was in marked contrast to the loud ovation accorded earlier to Argentine Foreign Minister Nicanor Costa Mendez who accused the United States of "turning its back" on Latin America and called on OAS member states to denounce Britain's "irrational armed aggression" and pressure the Reagan administration to return to a position of neutrality in the Falklands dispute.

In response to the Argentine request, several Latin American members of the 30-nation OAS were circulating draft resolutions that, in their most extreme form, would condemn Britain, urge the United States to stop aiding Prime Minister Margaret Thatcher's government and call for a cease-fire and resumption of peace negotiations.

Although it was not clear that a resolution explicitly attacking the United States would win necessary backing, there was no mistaking the bitterness evident in public and private comments of Latin American ministers at the meeting.

U.S. officials are especially concerned that Argentina will succeed in cutting across the ideological differences and other rivalries that traditionally divide many Latin American countries and unite them, in effect pitting Latin nations against what many openly are calling a "gringo" alliance of the United States, Britain and Western Europe.

Costa Mendez seemed to be openly inviting such divisiveness when he charged that the United States has "turned its back on the region in order to assist a European state, also Anglo-Saxon, also an atomic power, also a world power, in the prosecution of its criminal, aggressive, colonialist adventure."

Haig, seeking to avert a rupture that could cause severe and long-lasting damage to U.S.-Latin American relations, tried to strike a conciliatory tone in his reply.

Citing a "sense of anguish that it has not been possible to prevent this terrible conflict," he called it "a loss and and a failure of our generation" and asked: "Is there a country among us that has not counted itself a friend of both countries?"

But, while reaffirming that the United States remains neutral about sovereignty over the disputed islands, he defended U.S. policy on grounds that Argentina, which seized the Falklands April 2, had violated the principle of not using force to settle disputes and was subsequently inflexible toward efforts by the United States, Peru and U.N. Secretary General Javier Perez de Cuellar to mediate the dispute.

For these reasons, Haig asserted, Argentina's appeals for help under the 1947 Rio treaty of reciprocal hemispheric defense "do not well apply" to the Falklands conflict.

The United States is among 21 active OAS members that are signatories to the treaty, but the U.S. position is that because Argentina struck the first blow, it cannot claim itself the victim of aggression and be entitled to aid from the other signatory governments.

Haig warned that if other OAS members try to assist Argentina with weapons and supplies, they run the risk of broadening and prolonging the fighting. Although he mentioned no country by name, U.S. officials are understood to be concerned that at least two nations, Peru and Venezuela, may be preparing to send warplanes, missiles and other supplies to reinforce Argentina's dwindling stocks of materiel.

Such moves, Haig said, could tear apart the inter-American system and destroy OAS ability to resolve hemispheric disputes. He said, "We must search for ways in which we can all join to help bring about peace, not ask the Rio treaty mechanism to adjudicate a conflict for which it was not conceived."

The secretary noted that the U.N. Security Council has given Perez de Cuellar "a new mandate to search for peace" and added:

"The most important thing we could do here would be to give our unanimous collective support to that effort . . . . The time has come for older heads to accept the risks of compromise and the hazards of conciliation to bring the suffering and the dying to an end."

However, there seemed little likelihood that his appeals would make much headway against the strongly emotional climate of Latin American opinion. It has even seen the radical leftist government of Nicaragua, which had accused Argentina of conspiring with Washington for its overthrow, join public declarations of solidarity with Argentina's rightist military leaders.

Instead, there was a general sense in the OAS last night that Argentina will come out of the meeting with some formal expression of at least moral support.

The strongest of the draft proposals, backed by Peru, Venezuela and Panama, would meet Costa Mendez' calls for condemnation of Britain and criticism of the United States, as well as clearing the way for other countries to send aid to Argentina.

However, Mexico and Costa Rica were circulating a more mildly worded draft.