As the diplomatic standoff over the 16-year-old son of a prominent Soviet diplomat continued yesterday, White House officials said the State Department is remaining firm in insisting on interviewing the youth, Andrei V. Berezhkov, who may be trying to defect to this country.

"To the best of our knowledge he still is in this country and we are still seeking to interview him to find out just what his wishes are," White House counselor Edwin Meese III said yesterday on "This Week with David Brinkley" on ABC-TV.

Meanwhile, on Air Force One traveling to La Paz, Mexico, President Reagan's deputy press secretary, Larry Speakes, said, "We think what we are doing is perfectly legitimate and consistent with international law."

The Soviet Embassy here has refused the request for the interview, and one top embassy official charged in a television interview that the State Department's actions are "a gross violation of international law."

The youth is the son of Valentin M. Berezhkov, a first secretary at the Soviet Embassy and the sole representative here of an influential Soviet think tank on American affairs. The father is prominent on the local diplomatic scene and often served as a tour guide for influential visitors from the Soviet Union.

Yesterday, the whereabouts of the youth remained a mystery, as it has been since Thursday when letters, signed with his name, were received by the White House and The New York Times. The letter to the newspaper said, "I hate my country and it's sic rules and I love your country." The White House did not reveal the contents of the letter it received.

Federal authorities continued to stand guard yesterday at the Soviet Embassy's compound on Tunlaw Road in Northwest Washington, but their presence was less obtrusive than on Friday and Saturday, when agents had peered into the windows of departing vehicles.

In the interview yesterday, Meese called the situation "very delicate and sensitive. It's a diplomatic situation, but it's also a very human situation, and so it's one of those things I think we're just following at the present time, trying to see what the next move will be."

Meese added, "We have no power to go into the embassy property and interview him. I think if they tried to move him out of the country then we would see about what could be done."

Meese declined to speculate on what would happen if Soviet officials attempted to take the youth to Dulles International Airport. "I think that's a hypothetical question," he said. "I think the right people are watching this, and we're just going to have to leave it in their hands."

The current standoff recalled a confrontation in 1979 when the State Department insisted on interviewing Soviet ballerina Ludmilla Vlasova, after her husband, Bolshoi star Alexander Godunov, defected to this country.

The Soviets refused and escorted Vlasova to Kennedy International Airport for a Moscow-bound Aeroflot flight. For three days, the flight was blocked at the terminal until U.S. officials met with her and were satisfied she was leaving the country voluntarily.

The Berezhkov incident began Wednesday when the Soviet Embassy reported to the State Department that the youth had taken his family's car and was missing from their home. The family lives at Highland House West, at 4450 S. Park Ave. in Friendship Heights, just across the District line in Montgomery County. But Thursday morning the State Department was informed that the youth had returned home. U.S. officials later learned of the two letters, a government spokesman said.