There are probably few Americans who do not sympathize with the desire of a young Soviet youth to remain in the United States. But it is open to question how far and strongly the US government should press the case of Andrei Berezhkov. This is the 16-year-old son of a Soviet diplomat who wrote a letter to President Reagan and to the New York Times saying, ''I hate my country and its rules and I love your country.''
Given America's long history of providing haven to those who seek political asylum, it is understandable that the State Department should wish to speak with ''Andy'' to ascertain the facts of the situation. But the situation is a sticky one, legally and diplomatically, and the danger to be avoided is not to let domestic political considerations - i.e., public sentiment - overtake the legalities of the case. What is called for is quiet, rational discussion of the matter with Soviet authorities.
In strictly legal terms, the issue is a tangle. There is the Vienna Convention under which diplomats and their families are given immunity. Presumably this covers the right not to be interrogated - especially when the individual is in Soviet custody. Then there is the claim for asylum. Can a 16 -year-old effectively claim asylum or refugee status? In the case of Walter Polovchak, the Ukrainian teen-ager who refused to return home with his parents in 1980, a court ruled that he could remain in the US and placed him in the custody of his sister. But the Illinois Supreme Court ruled the parents had a right to custody of Walter if they came back to the US to get him.
Certainly there is strong American judicial sympathy for parents in cases of runaway children. Indeed it is hard to refute the general premise that parents should have custody of their children until the latter are capable of responsible decisions. Teen-agers often make snap or immature judgments only to reverse themselves later on.
We are reminded of a similar diplomatic case in 1955, when the teen-age son of a Soviet army officer crossed into the US sector of Berlin and refused to return to his parents. For three weeks he was feted by American officials as an anticommunist defector. But the issue aroused Moscow to the point where Foreign Minister Molotov intervened and President Eisenhower instructed his diplomats to reunite the boy with his family. The lad, meantime, had gotten homesick and changed his mind about defection.
The State Department must be aware of the potential consequences of the Berezhkov affair. If it escalates into an ugly incident, the Soviet Union could retaliate in some way against the families of US diplomats in Moscow. What would happen, say, if some US teen-ager got into trouble in a Soviet-bloc country? The Berezhkov case could come back to haunt Washington. Surely any negative repercussions are to be avoided, especially at a time when efforts are being made to halt the decline in US-Soviet relations.
The case is regrettable for another reason. The Soviets have been sending better people abroad. Andy's father, Valentin Berezhkov, a first secretary in the Soviet Embassy, represents this more cultivated breed of diplomat. Yes, he serves a communist government, but he has the reputation of being a decent man. His son returned to his parents, and reportedly did so voluntarily. But, whatever happens, one can only imagine the personal tragedy for Mr. Berezhkov, who will be held responsible for the behavior of his son.
Mr. Reagan, in short, would be wise to dispose of the case with minimum diplomatic damage. That may seem unfeeling of a Soviet youth's sensitivity to a free society. But in the long run an improved US relationship with the Soviet Union is the more vital consideration.