Carter administration officials yesterday described the verdict in the Moscow trial of U.S. businessman Francis J. Crawford as one in a series of hopeful signs that U.S. Soviet relations are on the upswing against after months of tension and acrimony.

The administration's public response to the Soviet action in suspending the five-year sentence given Crawford after his conviction for alleged currency violations was guarded. In private, though, senior officials said they regarded the outcome as a Soviet gesture toward easing some of the strains in recent dealings with Washington.

"No one's getting carried away by the idea that we're moving back into the palmier days of detente overnight," one official said. "But the Crawford verdict makes clear that there's pattern emerging again of basically positive rather than negative developments."

He and other officials said other significant elements of this pattern include Moscow's recent decision not to press to a showdown a libel action against two U.S. newsment in Moscow, the White House reaffirmation on Wednesday of its decision to permit the sale of sophisticated U.S. oildrilling equipment to the Soviets and renewed moves by both sides to achieve a breakthrough on a strategic arms limitations talks (SALT) agreements.

Within this context, the officials added, the outcome of the Crawford case was especially significant because his arrest in July had the symbolic effect of accelerating the decline in U.S.-Soviet relations into a rollercoaster-like downward plunge.

That point was underscored in the brief statement issued by the State Department yesterday. Its operative sentence said: "While we regard the action taken against Mr. Crawford as improper and unwarranted, this resolution will serve to remove what has been a serious impediment in Soviet American relations."

As recently as a few weeks ago, those relations were so strained that one senior U.S. official, rating them privately on a scale of one to 10, said they would rank no higher than three and were likely to drop even lower.

Underlying the tensions were a number of factors, including the tendency of President Carter and senior members of his administration to publicly criticize Soviet military activities in Africa and repression of dissidents within the Soviet Union.

The Soviet leadership, charging interference in its internal affairs, responded with such tactics as its attempt to crack down on reporting of dissident activities by U.S. reporters in Moscow and an escalating series of public attacks on such Carter administration policy makers as the president's national security affairs adviser, Zhigniew Braernald.

The situation was exacerbated further when the FBI arrested two Soviet citizens employed by the United Nations and charged them with espionage.Although the State Department advised that they be expelled, the decision was made to prosecute them.

That, State Department sources say, led the Soviets to retaliate by arresting Crawford. The incident, which saw Soviet police drag Crawford from his car on a Moscow street, brought U.S. Soviet relations to their lowest ebb in years and touched off a groundswell of public and congressional pressure for Carter to take an even tougher stance toward Moscow.

The administration responded with a number of measures, including a freeze on most high-level official trips to the Soviet Union and the holding up of several visas requested by Soviet bloc officials seeking to visit the United States. It also blocked pending sales to the Soviet of sophisticated computer equipment made by Sperry Rand and the oil-drilling equipment manufactured by Dresser Industries of Dallas - although the Dresser deal was given a green light on Wednesday.

While those much publicized measures were being carried out, State Department sources said, the administration also was trying to apply the carrot as well as the stick. As one official put it:

"We cooled down some of the rhetoric that the Russians had found annoying. We made it clear that, despite all the unresolved differences, we wanted to find areas of cooperation. We let them know that conciliatory gestures on their part would meet with an appropriate response from our side."

For example, he noted, the Soviet decision to let Crawford go free is likely to mean a reassessment within the administration of the moratorium on high-level U.S. visits. No decisions have been made yet, the official said; but he predicted a return to normal official traffic between the two countries in the very near future.

Another important factor, some officials said, was the attitude of the U.S. business community and its possible impact on the Soviet desire for increased U.S. trade. Said one official, "It was kept very discreet and low key. But the business people made it very clear that they'd have problems doing business in Moscow if their people there were to be used as hostages and pawns in political power plays."

Throughout the entire period, the officials stressed, the United States made clear that it would not consider a prisoner exchange involving the release of the two Soviet held here for Crawford or some other Soviet prisoner like the imprisoned dissident Anatoly Scharansky.

Although rumors of such a trade continued to be heard yesterday, senior department officials insisted that "no deal has been made or is in the works."