The first public dispute between the Soviet leadership and the Carter administration has apparently ended now and from here, at least, it looks like it was the Americans that came out a bit chastened.

The contretemps began last week after a Soviet prosecutor warned Andrei Sakharov, the dissident physicist and Nobel Prize winner, that he faced possible criminal charges if he continues his activities. Thursday, in an unusually forthright statement on so sensitive an issue, the State Department cautioned Moscow against attempting to "intimidate" or otherwise silence Sakharov.

The Kremlin reacted quickly. Soviet Ambassader Anatoliy Dobrynin complained in Washington that such support for the dissident was bound to be resented in Moscow. Over the weekend, the Soviet press carried a number of articles and angry commentaries asserting that any backing for dissidents is anti-Soviet and, what's more, the United States violates the human rights of its own citizens.

Finally, on Sunday, President Carter told reporters he had not approved the statement on Sakharov and that while it generally "reflected" his attitude, the State Department may have been remiss in not seeking his clearance. The implication, judged from this distance, was that the department had made a mistake - one that would not lightly be repeated. Secreatary of State Cyrus R. Vance followed up today with a similarly ambiguous seeming rollback.

From the Soviet perspective, the affair seems to illustrate a variety of important points, some obvious, others not so plain:

First, the administration is still very much in its infancy and some confusion over its positions is inevtiable. Thus, for instance, on the subjects of utmost importance to the Soviets - the Strategic Arms Limitation Talks - Carter and his spokesmen aired several ideas and possibilities last week that appeared in the end as perplexing as they did promising.

The most sophisticated view expressed here by Soviet analyst therefore is that these early pronouncements should not be considered binding.

Nonetheless, the Sakharov squabble shows that human rights in general and Soviet treatment of dissidents in particular are potential sources of friction between Washington and Moscow, assuming that Carter and his aides follow up their pledge to speak out against oppression.

The State Department would not have gone ahead with its original statement, the Soviets apparently feel, if the sentiments had not - to use Carter's term - "reflected" the President's view. Noting on Saturday that some senior officials in Washington were already backing away from the Sakharov statement the Soviet news agency Tass said.

"But fact is fact. The State Department, without thinking twice, issued a statement and an official one."

The Soviets have pledged through several emissaries to avoid anyserious confrontation with the Carter administration in its early months and there seems to be no reason now to doubt that the promise will be kept on vital issues of war and peace.

Yet, the warning to Sakharov may well have been a test of Washington's willingness to strain relations with the Kremlin on the thorny human rights question. The authorities did not casually summon Sakharov, the most famous disssident in Eastern Europe, to face a prosecutor's threats. They doubtless knew that the incident would receive wide attention in the West. Perhaps the Soviets wanted to see what would happen - and they found out.

The outpouring of Kremin critcism of the human rights record in the United States and other Western countries is by no means unprecedented. Whenever Moscow feels that the issue of Soviet rights is coming alive again, the press here speedily strikes back. So it was that on Sunday, Pravada's Washington correspondent Gennadi Vasilyev wroted an article on police surveillance of Americans.

"Massive police surveillance, files on millions of citizens and the violation of the rights of the individual is the reality in the United States, a country whose propaganda loves to hold forth on 'democracy' and 'civil liberties,'" he wrote.

Clearly on these ideological issues, the Kremlin has no plans for a honeymoon with President Carter.