The Carter administration held its ground yesterday against the strongest official Soviet complaint it has received over American support of Russian dissidents.

In the wake of President Carter's personal letter to leading Soviet dissident Andrei Sakharov, the Soviet Union cautioned against attempts "to interfere' in its affairs under "a thought-up pretext of 'defending human rights.'"

White House press secretary Jody Powell countered that "the Soviet Union has in the past exercised their right to comment on domestic differences within our own [country]."

The President "was not attempting to challenge the government of the Soviet Union," said Powell.

Powell said the President "was responding to a letter from a Nobel [Peace] prize winner," and he was acting "as the duly elected spokesman for the American people in what he perceives, and I believe correctly, to be their wishes in this matter."

There is also "a legal basis for any comments in the Helsinki agreement" on human rights, Powell said.

In comparing U.S. and Soviet comments on each other's domestic affairs, Powell cited a meeting of Soviet leader Leonid I. Brezhnev with American Communist Party leader Gus Hall, support in the Soviet newspaper Pravda for Communist Prof. Angela Davis during her California trial, and frequent Moscow Radio commentaries on U.S. affairs.

The crossfire between the Carter administration and the Soviet Union on human rights has been escalating for three weeks. President Carter's letter to Sakharov, made public by the Soviet physicist on Thursday, was an unprecedented message by a U.S. chief executive to a Russian dissident, In it Carter said the United States will "seek the release of prisoners of conscience."

Tass, the Soviet news agency, was first to disclose yesterday that Thursday night the Soviet ambassador to Washington, Anatoliy F. Dobrynin, called on Acting Secretary of State Arthur A. Hartman with a complaint.

Without mentioning either President Carter or Sakharov, Tass said Dobrynin "stressed . . . that the Soviet side resolutely rejects attempts to interfere under a thought-up pretext of defending human rights' in its internal affairs, in matters that fall within the competence of the states."

Tass said, "The Soviet side has a lot to say - and with good reason - concerning the state of affairs with the insurance of basic human rights in the United States, having in view unemployment affecting millions of people, racial discrimination, women's inequality, infringement of civil liberties of individuals, growing crime rates, and on . . ."

Attempts "to impose one's view on another side," Tass said, ". . . would only complicate them and make more difficult the solution of problems" between the two nations.

No reference was made to any specific problems. The largest issue on the current U.S.-Soviet agenda is resumption of nuclear arms control negotiations. At the State Department, spokesman Frederick Z. Brown said, "We believe other elements of our relationship with the Soviet Union should go forward on their own merits."

He said, "We obviously do not consider our statements to be interference in Soviet internal affairs."

Carter's decision to write Sakharov, in reply to Sakharov's appeal to him, troubles some experts on Soviet affairs as a hazardous involvement of the President's prestige. In response to inquiries about disagreement, State Department spokesman Brown said, "I want to put down any notion that there is any wave of dissent on this matter; that simply is not true."

"The State Department was involved throughout the whole process," said Brown, in "drawing up the letter and sending it." Powell, when asked if there is concern that Soviet suppression of dissidents may only intensify, as some specialists fear, said the administration would not have acted unless it thought what it was doing was right and the dissidents did also.

In Geneva yesterday, at a meeting of the United Nations Human Rights Commission, U.S. representative Allard K. Lowenstein said he will seek action Monday to express concern about Soviet detention of human rights campaigners. Soviet representative Valerian Zorin said the commission is "not entitled to discuss" internal Soviet affairs.

Vice President Mondale is scheduled to meet Tuesday with another Soviet dissident, exiled Vladimir Bukovsky, who was released in December. In addition, a meeting between President Carter and Bukovsky is "very likely," spokesman Powell said Thursday.