The Socialist government of Andreas Papandreou is seeking to close one of the four U.S. military bases in Greece on the argument that it is being used for the unauthorized surveillance of non-Warsaw Pact countries friendly to Greece, according to diplomatic sources here.

The Greek Socialists also have put a $1 billion annual price tag on the continued operation of the remaining three bases, the sources said, and these demands were expressed last month in writing during the first round here of negotiations on the bases' future. They reportedly were conveyed to Washington by the U.S. negotiator, Reginald Bartholomew.

The American response to the Greek demands is expected to be considered in the second round of the negotiations, which began here Thursday between Bartholomew and Yiannis Kapsis, Greek foreign affairs undersecretary.

The sources identified the base that the Papandreou government wants to close as the Hellenikon airbase, on the eastern outskirts of Athens. The three other major U.S. bases in Greece are Nea Makri, northeast of the capital, and Herakleion and Souda Bay on the island of Crete. The bases, established under an agreement between Greece and the United States in 1953, serve as staging and supply posts for American and NATO naval and air forces.

They also permit surveillance and monitoring in the Balkans and the eastern Mediterranean.

Military experts confirmed that Hellenikon's main functions are providing communications, logistical support for the other bases, strategic lift facilities for transiting military aircraft and electronic surveillance.

According to Greek officials, only 10 percent of the activity of the U2 aircraft carrying out this surveillance is directed toward the NATO-targeted Balkan countries to the north. The rest of the time the planes fly south and are presumed to direct their electronic eyes and ears toward countries such as Libya, they said.

Greece contends that this activity is not authorized by any written agreement on the use of the bases and that it started "illegally" during the period of military rule here between 1967 and 1974.

Sources close to the negotiations said the Papandreou government is willing to allow the other activities of Hellenikon to be transferred elsewhere, for example to one of the other three bases or ancillary U.S. military facilities scattered throughout Greece.

Spokesmen at the U.S. Embassy here said they had no knowledge of a demand for the closure of Hellenikon, nor of a demand for $1 billion in annual rent.

The Greek Socialists came to power 14 months ago on a platform of closing all U.S. bases in Greece. Since then, Papandreou has insisted on the goal of a timetable for the bases' removal, suggesting, however, that this would be a goal for the medium term instead of the immediate future.

Greece has indicated that it will try to extract a high price in terms of cash and military hardware from Washington for the bases' continued operation.

Government sources said Papandreou hopes renewed warmth in Greek-Soviet relations will help generate pressure for Greece's demands in bases talks. He received a delegation headed by the Soviet justice minister, representing the Soviet Communist Party, last week. According to diplomatic sources, Soviet Premier Nikolai Tikhonov is also expected to visit Athens early next year.

The Socialists also have said the 1953 agreement on operation of the bases will be suspended unless the negotiations bear fruit within nine months.

Talks on a new defense and economic cooperation agreement with the previous conservative government foundered, reportedly over Greek demands for high economic and military benefits, a few months before the elections that brought the Socialists to power.

But the bases continued to function under the 1953 agreement. Under this agreement, the bases' operation is linked to the duration of Greece's membership in NATO.