Soviet embassy officials here refused to accept a letter signed by leaders of the three major religious communities in this country protesting the recent trials and sentencing of dissidents in the Soviet Union.

Representatives of the National Council of Churches, the National Conference of Catholic Bishops and the Synagogue Council of America entered the embassy briefly Wednesday morning but embassy officials refused to accept their protest letter.

United Methodist Bishop James Mathews, representing the NCC, said the group, which had made an appointment in advance of their appearance at the locked gate, was received "courteously but coldly" by the embassy's first press secretary, Boris N. Davydov.

"He told us they regarded the trials as an internal affair and that there was nothing to discuss with us," said Mathews. "He declined to receive the document."

The trio, which included Msgr. Francis J. Lally representing the Catholic bishops' conference, and Rabbi Walter Wurzberger, vice president of the Synagogue Council, released copies of the letter to the press and agreed to try again to deliver a copy to the embassy by mail.

The letter, addressed to Ambassador Anatoly Dobrynin, protested "the arbitrary nature" of the recent trails of Soviet dissidents, and added that "we are shocked by the severity of the sentence imposed."

The letter was signed by William P. Thompson, president of the NCC; Bishop Thomas C. Kelly, general secretary of the bishops' conference; and Rabbi Saul Teplitz, president of the Synagogue council.

The dissidents named in the letter were Anatoly Scharansky, sentenced to 13 years imprisonment at hard labor; Aleksander Ginzburg, sentenced to eight years at hard labor; Vladimir Slepak, sentenced to five years of internal exile; and Victoras Petkus, sentenced to 15 years in prison and labor camps and to internal exile.

In their letter, the religious leaders noted that "as representatives of millions of Americans" they had "not hestitated to criticize our own government when warranted" and added: "We appear most earnestly for the release of the above-mentioned prisoners as well as others in similar circumstances. In the absence of such action, we fear a serious deterioration of the international climate, a development we are most anxious to avoid."

A potential squabble among the protesters erupted when two representatives of Soviet watchdog organizations appeared at the impromptu sidewalk press conference across the street from the embassy and demanded to accompany the religious leaders.

Sister Ann Gillen of the National Interreligious Task Force on Soviet Jewry and Rabbi James A. Rudin of the American Jewish Committee were permitted by organizers of the protest to make statements to assembled reporters.

Since their names were not on the list submitted in advance to the embassy in the request for the appointment, they were left behind as the three leaders were escorted into the building.