President Reagan said yesterday that the dispute between Argentina and Britain over the Falkland Islands is not an issue that justifies military confrontation, and he offered to help the two countries find "a peaceful resolution with no forceful action or no bloodshed."

Reagan's plea for moderation, made during an impromptu meeting with reporters at the White House, came as U.S. officials worked behind the scenes to prevent a clash that could have serious consequences for American policy by forcing the administration to choose sides.

The president and other U.S. officials, striving to maintain a neutral position, were careful to be noncommittal in public about possible U.S. moves. In private, administration sources said that Argentina's occupation of the Falklands appears to be an accomplished fact that cannot be reversed unless Britain resorts to force on a scale that would cause tensions for years.

The sources, who insisted on not being identified, conceded that the naval force dispatched by Britain to the South Atlantic probably could dislodge Argentine troops from the islands or, at the least, inflict a serious blow on Argentine forces in the region.

But, the sources continued, even if Britain succeeds in the short term, its victory would leave bitterness throughout Latin America and put Britain in the position of having to maintain a huge, long-term protective military and naval presence in the Falklands that would likely put heavy strains on its budget and the resolve of the British public.

For those reasons, the sources said, the United States hopes to find a formula that will acknowledge Argentine sovereignty over the islands and still be sufficiently acceptable to Prime Minister Margaret Thatcher's government to permit Britain to pull away from armed confrontation.

There has been considerable speculation about a compromise built around the idea of accepting Argentina's sovereignty over the Falklands while keeping them under British administration for a specified period.

However, the sources cautioned, at this point it is too early to say what kind of compromise might be worked out; and, as one person, noting the time it will take for the British task force to arrive on the scene, said, "We have approximately two weeks to play with it."

The administration's search for an opening came as Argentine Foreign Minister Nicanor Costa Mendez told a special meeting of the 28-nation Organization of American States that his government might ask its "brothers in the hemisphere," including the United States, to help it defend the Falklands against British "colonialism."

After suffering a rebuff Saturday when the U.N. Security Council called for withdrawal of the Argentine forces, the military government of President Leopoldo Galtieri is maneuvering to bring discussion of the dispute into the jurisdiction of the regional body, where it thinks it can get greater backing for its position.

Costa Mendez, while asserting that his country wants a peaceful solution, reiterated that the question of Argentine sovereignty is "not negotiable"; and he said his government is considering, in the event of a British attack, whether to invoke the 1947 inter-American treaty, which calls on signatory nations to help defend one another from attack.

The United States is a signatory to the Rio Treaty, as it is commonly known, and used it during the 1960s to win Cuba's suspension from the OAS and to justify U.S. intervention in the Dominican Republic.

In a remark clearly intended to put the United States on the spot by referring indirectly to these Cold War uses, Costa Mendez said:

"Perhaps the time has arrived to learn if the Rio Treaty is useful, or, as has been said, it is only an instrument for certain kinds of problems and directed against certain kinds of ideas."

That type of potential pressure appeared to be what Reagan had in mind when he said yesterday: "It's a very difficult situation for the United States because we're friends with both of the countries . . . . What we hope for is to have a peaceful resolution with no forceful action or no bloodshed."

The narrow line that the administration is trying to walk was underscored by State Department spokesman Dean Fischer, who acknowledged that the United States is bound by a 1962 agreement to make available to the British force the American airfield on Ascension Island in the Atlantic between Africa and South America.

Fischer put special stress on the legalities and added: "Such use of the airfield therefore does not in any way constitute U.S. involvement in the United Kingdom-Argentine dispute."