The State Department, still buffeted by the problems of dealing with 130,000 Cuban and Haitian refugees, is facing a deadline on another group of Latin exiles -- 10,000 Nicaraguans whose permission to stay here expires Monday.

The Nicaraguans, many of whom are supporters of ousted strongman Anastasio Somoza, face deportation proceedings if the Carter administration doesn't extend their stay. As yet, there is no sign they will be allowed to remain. So Robert L. Boyer, a Miami attorney for the group, said he plans to file suit to block any expulsions.

John Blacken, director of the State Department's Central American office, yesterday said that a decision on the Nicaraguans has not been made yet. He said the administration is concerned about the precedent that extending their stay would set for other groups seeking similar treatment.

Boyer said the group would like to be treated as refugees, or at least be allowed to remain in the United States like the 114,000 Cubans and nearly 16,000 Haitians the administration announced last week those refugees could stay.

"They (administration officials) gave the Cubans and Haitians an across-the-board dispensation. There shouldn't be disparate treatment of similar groups," Boyer said.

The situation facing the Nicaraguans is the latest problem the administration faces as it balances humanitarian and political considerations in treating exiles.

"These are the hidden refugees," Michael Maggio, a Washington immigration lawyer, said of groups staying here under "extended voluntary departure" status.

In the past, persons from Ethiopian, Iran, South Korea and other countries have been permitted to extend their legal stays in the United States because of unsettled conditions in their own countries, while applications for asylum were pending or after they had been rejected.

Maggio, is trying to get the administration to grant similar "extended voluntary departure" status to thounsands from El Salvador, whose country has been filled with civil strife in recent months.

Maggio was among a group of lawyers who first asked the State Department a year ago to allow Nicaraguans fleeing the war to stay in the United States. But the Carter administration didn't act until late June last year. Ironically, Maggio said, the main benefactors have been Somoza supporters.

The Carter administration has been trying to get along with the new Sandanista junta, lobbying vigouously to get an aid package through Congress.

Blacken said the State Department isn't that concerned with the Sandanistas' response to a U.S. declaration that the Nicaraguans could stay here. Dr. Rafael Solis, the new government's ambassador in Washington, yesterday said that the Sandanistas wouldn't object if the Nicaraguans visas are extended again.

He said some of the exiles, specifically generals of Somoza's national guard, would face charges if they return to their homeland. But those who aren't suspected of specific crimes are free to return, he said.

Boyer, the group's attorney in Miami, said as many as 2,000 of the exiles are members or relatives of Somoza's National Guard. He described the others as businessmen or middle-level civil servants.

He noted that many members of the group haven't applied for asylum yet because they felt their stays would be extended.

In recent years, more and more foreign citizens have applied for asylum in the United States. For instance, figures from the Immigration and Naturalization Service show that in 1978, 3,702 persons filed asylum requests. The number went up to 5,801 in 1979. And a state department official estimated that more than 10,000 will apply this year -- in addition to the 130,000 Cubans and Haitians who applied before being granted special permission last week to stay permanently in the country.

Persons who file for asylum can't be deported until their cases are considered. The State Department has such a hugh backlog of asylum cases that it is now assigning extra officers to work on them, an official said yesterday.