The Carter administration cautioned the Soviet Union yesterday that the outcome of trials of Russian dissidents Anatoly Scharansky and Alexander Ginzburg would be treated by Washington as "an important indicator" of American-Soviet relations.

Reading a statement approved by the White House, State Department spokesman Hodding Carter expressed "deep concern" over the sudden announcement in Moscow that the trials would begin on Mondays. "These trials will be watched closely in the United States," he said.

The Soviet Union announced yesterday that Scharansky will be tried on charges of high treason, which carry a possible death penalty, and Ginzburg on charges of anti-Soviet propaganda - a possible 10-year prison sentence.

But Carter repeatedly declined to characterize possible American reactions to the trials and refused to link the cases specifically to strategic arms limitation talks. He announced that Secretary of State Cyrus R. Vance would go ahead with next week's scheduled meeting with Soviet Foreign Minister Andrei Gromyko in Geneva on a new arms limitation agreement and other topics.

The evident care with which the State Department addressed the opening of the trials reflected long-standing concern by administration officials that Moscow could use the cases to challenge the credibility of President Carter and his human rights campaign. This could bring new strains in American-Soviet relations, already at a precarious point over American outcries against Soviet and Cuban military involment in Africa.

The president publicly insisted last year that Scharansky had never had any ties to the CIA, a charge leveled against the 30-year-old computer expert by Dr. Sanya L. Lipavsky, a Russian Jewish doctor subsequently identified in American press accounts as a former part-time agent for the CIA in Moscow.

Scharansky and Ginzburg were major figures in the group of dissidents monitoring Soviet compliance with the Helsinki human rights accord. Scharansky, who was seized in March 1977, also became a spokesman for Soviet Jews after he was refused permission to emigrate to Israel.

The National Conference on Soviet Jewry, representing 39 U.S. Jewish groups, cabled yesterday asking Vance to cancel his meeting with Gromyko to protest the announcement of the trials. B'nai B'rith International will issue a statement Sunday condemning the trials as part of "an anti-semitic campaign."

The State Department admonition said that the fate of the two men "will be an important indicator of the attitude of the Soviet government, both with regard to observing its commitments under the Helsinki Final Act and to promoting a healthy atmosphere for the constructive development of U.S.-Soviet relations."

The spokesman condemned soviet refusal to let Scharansky see family or friends since his arrest or select his own lawyer. "These factors call into question the fairness of the trial and the protection of Mr. Scharansky's human rights," Carter said. He added that the U.S. government would not offer further comment while the trials were in session.