The State Department said yesterday it has recommended that thousands of Nicaraguan exiles who fled to the United States during last year's political turmoil be given an additional 90 days before they must either leave this country or apply for political asylum.

Permission for the Nicaraguans to remain in the United States expired yesterday. But department spokesman Hodding Carter said the 90-day extension would give them time to put their affairs in order.

The extension was the third granted to the Nicaraguans since they fled the civil war in their country. Other officials said this latest reprieve would be the last. The exiles, who have been allowed to work here during their stay, can either go back to Nicaragua, go someplace else, or apply for asylum here.

Officials said privately however, that they "do not intend to throw people out" whose cases for political asylum are still pending at the end of the 90-day period.

Many of the exiles are supporters of ousted president Anastasio Somoza. Carter said those who fear persecution if they return to Nicaragua can apply for asylum and their cases will be reviewed individually.

Officials last week said there are about 10,000 Nicaraguan exiles in the United States. But yesterday Carter said the government wasn't sure of the number.

The State Department recommendation on the extension was contained in a letter sent to the Immigration and Naturalization Service last Friday by Deputy Secretary of State Warren Christopher.