U.S. officials sought anxiously yesterday for ways to forestall a military clash over the obscure Falkland Islands that might force this country to choose between a suddenly aroused Britain, its closest global ally, and inflamed neighbors in South and Central America.

Although it struck many as a cross between a 19th century melodrama and a Peter Sellers farce, the British-Argentine struggle was no laughing matter at the White House and State Department, where policy makers are paid to take seriously any threat of war between nations. They must be, and were yesterday, especially concerned about conflicts that could have substantial consequences for the United States.

Given the steaming time and readiness of the British fleet, Washington officials estimated that they have about two weeks to head off a major military engagement in the South Atlantic. But as of now, there is no clear plan within the administration for averting that collision.

"This is a no-win situation for the United States," said an official, pointing out that its close and longstanding "special relationship" and NATO alliance with Britain would be in a tug of war with U.S. interests in Latin America and possibly even its commitments tohemispheric defense under the Inter-American Treaty of Reciprocal Assistance, or Rio Treaty.

The North Atlantic Treaty Organization bond could not be invoked to bring the United States to the side of the British because the Falkland Islands and the nearby South Atlantic are outside the bounds of NATO, officials said. Nevertheless, Britain clearly expects U.S. backing in the spirit of alliance, much as the United States expected British backing when American diplomats were seized and held hostage in Iran.

A senior State Department official expressed doubt that the Rio Treaty could be invoked by Argentina to defend itself against a British attack on the Falklands, because it is legally uncertain that this is Argentine territory. The United States, the official said, has carefully refrained from making an official judgment about sovereignty in the Falklands.

Whatever the treaty obligation, however, there is little doubt that most or all of Latin America would line up in passionate opposition to British military action to retake the island to retaliate against Argentina. If the United States were seen to be cooperating, the backfire in the hemisphere could seriously affect administration efforts to build regional solidarity against Cuba, Nicaragua and leftist influences in Central America.

The basic confict between Britain and Argentina over the Falklands is a longstanding one, but the possibility of a military clash became more serious in the last year or two, according to State Department officials.

The first warning of imminent military action by Argentina came last Tuesday from British sources, officials said. Washington responded within a few hours with an urgent diplomatic inquiry to Buenos Aires reporting the receipt of "very disquieting intelligence" and asking for assurances that no Argentine military action was planned.

When the reply was not reassuring, further contacts were initiated, culminating in President Reagan's 50-minute telephone call Thursday evening to Argentine President Leopoldo Galtieri.

Reagan told Galtieri, according to a source, that Congress and the American people would consider Argentine action to be aggression, with potentially important consequences for U.S.-Argentinian relations.

In a reference to the possible military consequences, Reagan reportedly warned Galtieri that British Prime Minister Margaret Thatcher is a determined leader who could not be expected to accept such action. He also said, according to the source, that he was convinced Argentina's use of force would be met by force from Britain.

White House sources described Reagan's call as a good-faith effort to head off the clash, saying that Reagan believed he had a reasonable chance to do so at the time. It is now clear, officials said, that Argentinian forces had already landed on the islands when Reagan sought to intervene.

Policy makers were conferring yesterday about further ways to use U.S. influence. Despite yesterday's call by the U.N. Security Council, it was considered uncertain that the world organization can be of much effect. The Organization of American States, which some in the administration favor turning to, said its council would meet tomorrow to hear Argentina's foreign minister. A prolonged round of OAS oratory might find an approach for a face-saving compromise, but senior officials at State fear the oratory might generate more passion than it dispels.

There is little expectation among officials that Argentina, having decided to send in its troops, will be easily persuaded to withdraw. At the same time it was believed that Britain has the military power to retake the islands should it be determined to do so, and it appears to be determined at the current time.

The likely basis for negotiations, and just about the the only bright spot, is that Argentina appears willing to discuss any aspect of the Falklands other than its claim to sovereignty. For Britain, sovereignty over this faraway real estate appears to be far less important than national pride and the fate of the 1,900 island residents.

Finding a way to reconcile Argentinian claims of sovereignty and British pride, in the face of powerful nationalistic sentiments stirred in both nations, was the formidable aim under discussion by U.S. policy makers yesterday.