President Carter delivered a strong message to Soviet President Leonid Brezhnev yesterday, protesting both through public remarks and private diplomatic channels the trials of dissidents Alexander Ginzburg and Anatoly Scharansky.

Secretary of State Cyrus Vance conveyed a personal message from the president to Brezhnev during a private meeting with Soviet Foreign Minister Andrei Gromyko that followed a day of lengthy discussions on limiting strategic nuclear arsenals.

State Department spokesman Hodding Carter declined to disclose the test of the protest message to reporters.

Carter, in an interview with four European journalists that was released by the White House earlier in the day, condemned the treason trial of Scharansky in strong terms, labeling it "an attack on every human being . . . who believes in freedom."

There was no doubt that the trials were a complicating factor hanging over the Soviet-American dialogue here on the weapons of annihilation which the two superpowers share.

When they finished their four hours of SALT talks yesterday, however, both Vance and Gromyko said it was too early to tell whether they would be able to make progress toward a new arms control agreement in the current atmosphere.

Through his spokesman, Vance characterized the talks as "businesslike and serious" without suggesting any advances had been made. The hope was left open, however, for at least modest progress in a concluding round scheduled for today.

Carter, in his interview with the European journalists, insisted that the United States will "never let anything interrupt our effort" to achieve a new SALT accord.

"The allegation that Scharansky was a spy for the United States is patently false," the president declared. "The Soviets know it to be false. They are prosecuting Scharansky because he represents an element, a small group, in the Soviet Union who are fighting for the implementation of international [human rights] agreements which the Soviets themselves have signed."

Asked if he intended to take any further actions in this matter, the president said:

"Well, there are other actions that are being considered, but of course we have no mechanism by which we can interfere in the internal affairs of the Soviet Union, nor determine the outcome of the trial, nor determine the punishment, if any, which is allocated to Mr. Scharansky.

"But we will continue through every legitimate means to let the Soviets know of our displeasure and also to work toward the minimization of any punishment meted out to him."

State Department spokesman Hodding Carter said the president's message of protest to Brezhnev was delivered by Vance to Gromyko in a short, private meeting lasting less than 30 minutes.

As he and Vance left the meeting, Gromyko would not acknowledge to reporters that the trials had been discussed. Earlier he abruptly refused to comment publicly on the potential impact of the trials on a new strategic arms agreement.

"I do not want to speak on this subject," said the veteran Soviet diplomat to a question by CBS correspondent Marvin Kalb. To stop the journalist from persisting, Gromyko added sternly, "Do you understand me correctly?" When Kalb acknowledged that he did, Gromyko slapped his palms together as if to brush off the topic and said, "Finish."

Spokesman Hodding Carter would not describe Gromyko's reaction to Vance's presentation on the dissident question.

Officials in the Vance party were irritated, some to the point of anger, by published interviews quoting U.S. Ambassador to the United Nations Andrew Young that seemed to minimize the importance of the Soviet crackdown. These officials expressed fear that the remarks by Young - who is in Geneva on U.N. business - would undercut Vance's efforts to make a strong human rights protest to Soviet leaders. The State Department spokesman, in an unusual action, rebutted statements by Ambassador Young point-by-point in response to questions.

Carter went out of his way to say that statements about the current trials and human rights conditions in the Soviet Union by the president and secretary of state aret he definitive expressions of U.S. Policy. He suggested that Young's statements on the subjects are not.

At the opening meeting of the two delegations yesterday morning, Vance presented U.S. views on the key remaining issues of strategic arms limitation for about an hour. Rather than respond immediately, Gromyko asked for a recess in the talks to compose the Soviet reaction.

The two officials, flanked by advisers on either side of long table, continued the arms discussion for about three hours in the afternoon.

Further discussion of strategic arms is scheduled for a meeting to start this morning and, if necessary, continue in the afternoon. Other issues such as the Middle East and Africa are also expected to be discussed.

In keeping with the strained state of U.S. Soviet relations, no joint luncheons, dinners or other social occasions have been planned for the delegations during the two days of talks.

Spokesman Carter said the absence of social activities by "mutual consent."