BUENOS AIRES, JUNE 14 -- Following Margaret Thatcher's election victory in Britain, the president of Argentina has expressed hopes that a solution can be found to settle the Falkland Islands conflict, which brought his country and Britain to war in 1982.

Congratulating the British prime minister on her victory, President Raul Alfonsin also disclosed that both the United States and Switzerland have been acting as unofficial mediators in quiet efforts to resolve the dispute.

"Switzerland wants to insist on the possibility of a dialogue between Argentina and Britain. . . . The United States is also working very hard on the matter," the Argentine leader told reporters aboard an airliner on his return to Buenos Aires from Europe this weekend.

Alfonsin did not give any details about the efforts by the two mediators to promote talks, adding only that so far there is "no definite project" to report. He described himself as neither optimistic nor pessimistic about the chances of negotiations. He said, however, that Swiss President Pierre Aubert was more optimistic now than before.

A senior Argentine official said privately that the Reagan administration has recently taken an increased interest in helping to make peace between Argentina and Britain. He linked this to heightened concern among National Security Council officials and others in Washington over the security implications of continued tensions in the South Atlantic.

Last year, Argentina granted the Soviet Union and Bulgaria rights to fish in its territorial waters. This prompted Britain to announce it would start enforcing the rights it claims to waters around the Falklands, raising the threat of a new confrontation between Argentine and British patrols.

Britain broke diplomatic relations with Argentina after Argentine troops invaded the islands in April 1982 under the military regime then in power. Since taking office in December 1983, Alfonsin's democratically elected government has sought talks with London on the issue. But Argentina's demand that the question of sovereignty be included on the agenda has repeatedly been rejected by Britain.