Secretary of State Alexander M. Haig Jr. yesterday urged the agitated countries of Latin America not to let their sympathies for Argentina inflame the Falkland Islands crisis and make more difficult "at this critical hour" U.S. efforts to mediate the dispute between Britain and Argentina.

But his brief plea to the 30-nation Organization of American States elicited only stony silence from the foreign ministers and ambassadors gathered here for a special meeting to consider Argentina's charges of aggression against Britain.

The reception given Haig stood in stark contrast to the tumultuous standing ovation accorded by the delegates a few minutes earlier to Argentine Foreign Minister Nicanor Costa Mendez, who called on the OAS to demand that Britain withdraw its battle fleet from the South Atlantic.

However, while the three-day OAS meeting appeared certain to turn into an orgy of fiery affirmations of Latin American support for Argentina and condemnation of Britain, most delegates privately seemed agreed that the meeting will not result in the OAS' adopting any collective punitive measures against Britain.

Even Costa Mendez, apparently reflecting Argentina's realization that it can expect no more than moral support from the rest of Latin America, stopped short of asking the organization to come to his country's aid under the collective-security provisions of the 1947 Rio Treaty and impose sanctions against Britain.

In short, the indications are that the OAS meeting, while it undoubtedly will create a lot of noise, is likely to have little impact on the unfolding of the Falklands situation and that the only hope of resolving the dispute without widened warfare rests in U.S. efforts to get its mediation diplomacy back on track.

Haig's three-week exercise in intercontinental shuttle diplomacy received a setback Sunday when Britain attacked the small Argentine garrison on South Georgia island and Argentina broke off, at least temporarily, the negotiations Haig had been conducting between the two governments.

In his OAS speech, Haig ignored increasing pressures in this country to side openly with Britain and sought instead to reaffirm what he said was President Reagan's belief that the United States has "perhaps a unique ability" to be the mediator.

He concluded by saying: "In the search for a solution, the United States remains at the disposition of both parties. At this critical hour, we are redoubling our efforts. With your help, we may succeed."

Haig acknowledged that Argentina feels frustrated by its inability to establish its claim to sovereignty over the Falklands--or Malvinas, as the Argentines call them--through negotiation. But he also made unmistakably clear the U.S. view that Argentina provoked the crisis by forcibly occupying the islands on April 2 and that it therefore cannot be considered a victim of aggression under the provisions of the Rio Treaty.

"There has been a use of force by an American state already," he said without mentioning Argentina by name. "This organization, and the world community, long ago made the determination that force shall not be used to settle international disputes. We shall all suffer if this principle, which the Rio treaty is designed to protect, is ignored."

The best path to a solution, Haig asserted, rests in the U.N. Security Council resolution, adopted April 3, calling for withdrawal of Argentine forces from the islands, a refraining by both sides from hostilities, and negotiations to work out the short-term and long-range status of the Falklands.

Haig said those are the goals the United States has sought to achieve through his shuttle mission.

But there was no sign of whether Argentina will abandon its refusal to deal with Britain, even indirectly, and consider the new U.S. proposals put together by Haig during meetings here last week with British Foreign Secretary Francis Pym.

Before the start of the OAS meeting yesterday, Haig and Costa Mendez did have the meeting that was abruptly postponed by the Argentines on Sunday, and sources on both sides said it went well.

However, the sources, noting that Costa Mendez is essentially a conduit for the military government in Buenos Aires and has limited powers of negotiation, said it was still unclear last night whether Argentina's rulers will choose renewed negotiations or let the situation drift toward further armed conflict.

Costa Mendez gave no sign of a conciliatory attitude in his speech, which bristled with denunciations of Britain as an "aggressor," "colonialist power" and enemy of the Third World. His voice rising in defiance, he shouted, "The invader shall learn that the Americas are not the land of vassals."

"The Argentine flag, which is the flag of the Americas, shall not be taken down while a drop of blood remains in the veins of the last Argentine soldier who defends the Malvinas islands. To this, I commit the honor of my country."

The closest he came to asking for specific help was an appeal for Latin America to demand that Britain withdraw its fleet from American waters and for Britain's partners in the European Economic Community to lift the economic sanctions they have imposed against Argentina. Even in regard to those matters, he made no formal request.

That appeared to be a tacit acknowledgment that Argentina cannot muster the votes required to get an OAS resolution with any real teeth. Of the active OAS members, 21, including the United States, are signatories of the Rio Treaty, and two-thirds of them would have to approve any resolution calling for diplomatic, economic or military sanctions.

Instead, the behind-the-scenes consensus at the meeting was that Argentina, at best, will be able to get a resolution supporting its position in general terms.

But some sources speculated that, despite the feeling of Latin American governments that they must support Argentina rhetorically, it might not be possible to go beyond the noncontroversial resolution adopted at the outset of the meeting yesterday, calling on both countries to avoid the use of force.