The Carter administration, using its strongest language since the start of the bloody civil war in Nicaragua, yesterday urged President Anastazio Somoza to accept mediation of the conflict in his tiny Central American country.

A public statement issued by the State Department noted calls by some of Somoza's opponents for a cease-fire and a "mediated solution" to fighting there and added:

"Given the mounting bloodshed, violence and suffering - and the growing disruption of national life - we believe that the appeal should be urgnetly heeded."

"We urge the government of Nicaragua to accept mediation and seek an enduring resolution of the crisis. We urge all concerned to accept a cease-fire and to be prepared to make concessions and sacrifices to bring an end to the suffering of the people of Nicaragua," the statement said.

Although department official insisted that the United States remains neutral in the Nicaraguan conflict, the statement had the net practical effect of putting a distance between Washington and somoza, whose family has ruled Nicaragua for 45 years - most of that time with strong U.S. support.

Any mediated solution acceptable to Somoza's foes would require considerable loosening of the iron grip that he and his military force, the national guard, have long exercised over Nicaragua. Most probably, such a solution would mean Somoza's surrender of the presidency.

It's an open secret within the State Department that most officials dealing with the Nicaragua situation believe that the best hope of ending the conflict would be offered by Somoza steping aside.

Otherwise, the officials believe, the fighting is almost certain to continue and lead either to a victory by the more extreme leftist rebels fighting Somoza's forces in the countryside or to a takeover of power by elements in the national guard advocating measures equally as repressive as Somoza's.

But, while U.S. officials clearly would like to see the government in the hands of a broad-based coalition of Nicaragua moderates, the Carter administration so far has refrained from taking any steps designed to pressure Somoza into resigning.

Instead, for the present, the administration is pinning its hopes on the idea that Somoza and most of his opponents can be induced to accept mediation, preferably with the primary role being played by other Latin American countries.

Washington sees the Organization of American States as the best mechanism through which carry out this mediation effort. Yesterday, the CAS, after two weeks of delay, agreed to meet on Monday and consider whether it should convene a meeting of foreign ministers to discuss Nicaragua.

The call for a ministers' meeting was made by Venezuela with the backing of the United States and several other hemispheric democracies. Their hope is that such a meeting could develop an acceptable means for the OAS or some of its individual member nations to enter the Nicaragua conflict in a mediating role.

Many diplomatic sources are skeptical that such an approach can work. Feeding their doubts are a traditional Latin American hostility toward outside interference in any country's internal affairs and the fact that many OAS countries are ruled by military dictatorships who might view such a precedent as a weapon that someday could be turned against them.

But U.S. officials mindful of President Carter's promises that the United States will not intervene overtly or covertly in other nations, say mediation, with Latin Americans playing the leading role, currently seems the only viable means of ending the fighting.

In another action yesterday, the OAS agreed to send a three-man observer team to Costa Rica to investigate that country's complaints about Nicaragua invading its territory.

Nicaragua also agreed to the observer mission, arguing that Costa Rica is serving as a refuge for the leftist guerrillas fighting Somoza and contended that any border crossings were the result of "hot pursuit" of rebels fleeing back into Costa Rica.