The village of Glen Cove, N.Y., today charged that a 36-acre Soviet estate there is an elaborate Soviet listening post operated by the KGB and is not entitled to the tax-exempt status normally granted diplomatic residences and consulates.

Glen Cove asked a federal judge in Brooklyn to overturn a 1971 court order granting tax-free status to the Soviets' Long Island estate, called Killenworth.

"Killenworth is in fact an elaborate, highly sophisticated electronic listening post operated and controlled by the KGB," the city said in court papers.

The surprise court motion, which city officials said was prompted by the downing of the South Korean airliner three weeks ago, was filed as representatives of Glen Cove and the Department of Justice clashed here over whether the Soviets connected with Killenworth should have access to Glen Cove's beaches and other recreational facilities.

John Chase, city attorney for Glen Cove, said that the motion to overturn the court decision is unrelated to the Justice Department suit. The Korean incident "definitely brought everything to the forefront," Chase said.

As evidence of espionage, Glen Cove cited news reports about the facility and a May 6, 1982, letter from FBI Assistant Director Edward J. O'Malley.

That letter to Glen Cove Mayor Alan M. Parente states that in the FBI's "experience . . . all Soviet establishments in the United States provide cover for a wide range of Soviet intelligence activities, and there is no reason to believe the establishment in your community is an exception."

At a time of increasingly strained U.S.-Soviet relations, lawyers for the Justice Department are in the position of arguing against efforts to ban Soviets from Glen Cove beaches.

"The United States is being deprived of its constitutional authority in foreign relations," said Justice Department attorney Catherine Coleman.

She was joined at the hearing by two representatives of the State Department.

But Chase argued that it is "hard to understand" how the State Department could praise the decisions last week by the governors of New York and New Jersey to bar Soviet Foreign Minister Andrei A. Gromyko from arriving in an Aeroflot plane at civilian airports in their area.

Coleman also argued that under federal law the estate is a residence and that the Soviets are, therefore, entitled to the same city privileges as its other residents. She also warned that any effort to take depositions from U.S. officials about the estate is "going to get into highly classified material."

The Justice Department sued Glen Cove a month ago over the city's 1982 order revoking Soviet access to beach and other recreational facilities.

Three weeks ago U.S. District Court Judge Joseph McLaughlin worked out a compromise allowing the eight permanent Soviet residents of the estate access to the beach, a move which effectively bars from the beach another 250 Soviet diplomats who had been visiting the estate on weekends.

In retaliation for the Glen Cove moves, the Soviet government has blocked U.S. diplomats stationed in Moscow from using a "diplomatic beach" there, and has raised to several thousand dollars fees those U.S. representatives must pay to use several Moscow sports facilities.

McLaughlin did not rule on the arguments and did not indicate when he will issue a decision.