President Reagan, saying he is "concerned for the health" of physicist Andrei Sakharov and his wife, appealed to Soviet leaders yesterday to end the conflict that has caused the couple to stage a prolonged hunger strike.

In a brief and deliberately low-key statement issued by the White House, Reagan said "I . . .strongly urge the Soviet government" to allow Mrs. Sakharov's daughter-in-law, Liza Alexeyevna, to join her husband in the United States.

Administration officials said the statement was made after several days of careful deliberation about whether it would help or hinder the Sakharovs' plight. The president's decision to speak out publicly appeared to indicate growing concern in the administration that the Sakharov situation, if not quickly resolved, could become a source of major new tensions between the United States and the Soviet Union.

Until yesterday, the main thrust of U.S. efforts to intercede with Soviet leaders on behalf of the Sakharovs had been to rely on quiet, behind-the-scenes diplomacy. In response to questions, State Department officials had conceded there had been several "high-level exchanges" on the subject, but they refused to describe details of these discussions.

However, informed sources privately said yesterday that the chief U.S. tactic in these exchanges had been to appeal to the Soviets "on humanitarian grounds" and to avoid pressure tactics such as threatening to cut off scientific exchanges if Sakharov dies or suffers serious health problems as the result of his hunger strike.

Prior to yesterday, the sources continued, the major U.S. representation took place Nov. 27 in a meeting between Walter J. Stoessel Jr., undersecretary of state for political affairs, and Alexander A. Bessmertnykh, minister-counselor of the Soviet Embassy here.

In that meeting, the sources said, Stoessel noted that if Sakharov dies or becomes seriously ill, the effects on American public opinion would be so adverse that there would be little hope for improvement of the already strained U.S.-Soviet relations. But, the sources also stressed, Stoessel was very careful to avoid making any threats and emphasized that U.S. interest in the situation is prompted by humanitarian considerations.

Underlying this approach, the sources said, is awareness that, where the treatment of Soviet dissidents is concerned, the Kremlin traditionally has been reluctant to yield to outside pressures. As a result, the sources added, the administration, despite its past tendency to take a hard line toward the Soviets, decided to forgo tough rhetoric and take the path of quiet diplomacy.

In this, the administration has been aided by the groundswell of protests and appeals that has sprung up in scientific, political and humanitarian circles in the United States and in other countries and has confronted the Soviet Union with a potentially serious problem about its image in the world community.

U.S. officials say there has been no governmental effort to coordinate or fan these private efforts to intercede for the Sakharovs. But they note that in this country, it has cut across ideological and political lines from left to right, and the officials added that former presidents Carter and Ford are considering making their own appeals to the Soviet leadership.

According to the sources, the administration hopes, most immediately, for a resolution of the dispute over Alexeyevna that will end the hunger strike. Looking beyond the immediate problem, the sources continued, the administration hopes further that the Soviets will attempt to end their continuing problems with Sakharov--problems that have a potential impact on East-West relations--either by ending his banishment to the industrial city of Gorki or possibly by expelling him from the Soviet Union, as it has done with other prominent dissidents.