The Organization of American States last night approved a greatly weakened version of a U.S. appeal for mediation of the bloody civil war in Nicaragua.

A special foreign minister-level meeting of the 25-member OAS debated the proposal until late yesterday before participants voted approval of the compromise measure calling on Nicaragua to accept "the friendly cooperation" of OAS members.

That was a drastically watered-down version of the original U.S. proposal for OAS members to offer to mediate "an enduring and democratic solution" to the Nicaraguan strife and for the OAS human rights commission to investigate alleged atrocities by the forces of President Anastasio Somoza.

However, the U.S. plan ran into the unyielding resistance of Latin America's military regimes, who charged that it would violate the OAS charter's prohibition against intervening in the internal affairs of hemispheric countries.

When it became apparent that the U.S. resolution could not muster the 17 votes needed for approval, a special negotiating group worked out the weak compromise that was adopted last night.

U.S. officials said they would be satisfied with the compromise resolution because, despite its weakened language, it would provide a loose framework for trying to induce Somoza to accept mediation of his dispute with domestic foes.

The Nicaraguan president, whose family has ruled Nicaragua for 45 years, appears to have effectively crushed, for the moment, the leftist rebels fighting his troops. However, U. S. officials say they believe the opposition to Somoza is so deep-seated that tensions are certain to erupt into new violence unless changes are made in the political situation there.

Washington has said repeatedly that the best path to these changes lies in mediation, and U.S. officials said yesterday that the compromise resolution keeps this principle intact in a way acceptable to a majority of the OAS, including Nicaragua.

Although the compromise makes no mention of mediation - using instead the more oblique phrase "friendly cooperation" - it does call for efforts to "find a peaceful solution to the situation without delay."

Similarly, U.S. officials said, the compromise also preserves Washington's desire for an investigation by the human rights commission of the atrocity allegations.

While the compromise resolution strikes out a request for the commission to prepare a special report on the atrocity charges, it does note that the commission is scheduled to visit Nicaragua shortly and asks that it expedite the trip "if possible."

In a related development, a bipartisan group of 78 members of Congress - including House Majority Leader Jim Wright (D-Tex.) - sent a letter to President Carter calling for support of Somoza.

The letter called Somoza "a long and consistent ally of the United States" and urged Carter "to take immediate steps to correct the misguided application of your policies by the Department of State." That was a reference to the fact that State Department officials dealing with the situation are known to believe that Somoza should step aside.

The legislators called Somoza's opponents "Marxist revolutionaries" and said their goal "is to make Nicaragua the new Cuba of the Western Hemisphere."

The majority of those signing the letter are known for a generally conservative stance in foreign policy. The first two signers - Reps. John M. Murphy (D-N.Y.) and Charles Wilson (D-Tex.) - are the two most active and vocal congressional members of the loose-knit, pro-Somoza forces in Washington referred to frequently as "the Nicaragua lobby."