Secretary of State George P. Shultz and Soviet Foreign Minister Andrei A. Gromyko had a lengthy get-acquainted session here today, but the meeting and another scheduled for Monday are not expected to contribute much toward easing the badly strained relations between the two superpowers.

A brief statement issued after the three-hour session said only that the two men "exchanged views on matters of concern to both countries" and will meet again Monday to discuss topics not covered today.

Later, a senior U.S. official, speaking to reporters on condition that he not be identified, refused to discuss the substance of the talks but characterized them as "serious and nonpolemical. They were two serious people discussing serious subjects, but I can't say there was any sudden, newfound friendship."

The two men met at a time when President Reagan appears more determined than ever to pursue his hard-line insistence that any return to the detente spirit of the early 1970s must be tied to Soviet willingness to modify what the administration regards as aggressive behavior in places such as Poland, Afghanistan and Central America.

However, since Soviet President Leonid I. Brezhnev's long term of leadership is in its twilight phase, Moscow is generally regarded as locked into passive, mark-time policies unlikely to undergo any dramatic change until Brezhnev's succession is decided.

Asked at his Washington news conference tonight about the state of U.S.-Soviet relations, Reagan said: "I think there's a pretty good understanding on their part as to where we stand." And he suggested that his administration had stopped Soviet expansionism. " . . . They haven't expanded into an extra square inch since we've been" in office, the president said, seeming to contradict past assertions by his aides that leftist forces were on the move in such regions as Latin America.

U.S. officials and other diplomatic observers see little hope of any substantive movement coming out of the Shultz-Gromyko talks.

Even the one area of fresh negotiations between the two countries -- the parallel talks under way in Geneva on reduction of intercontinental and medium-range nuclear weapons -- is in a very preliminary stage, with the two sides far apart and any expectation of progress far down the road.

The senior official said that while these negotiations were the subject of much discussion today, the talk was "more in the nature of a review" than breaking new ground.

Similarly, the interest expressed by the administration a few months ago in a Reagan-Brezhnev summit has waned to the point where U.S. officials now regard the idea as unlikely and not particularly desirable. In fact, the senior official said Shultz and Gromyko did not even discuss a summit today.

As a result, the main importance of today's meeting was the opportunity it presented for the two men to take each other's measure and begin establishing a basis for future dealings. Shultz is the ninth American secretary of state to negotiate with Gromyko, who has been in his post since 1957.

The last meeting on this level took place here in late June when Gromyko conferred with Alexander M. Haig Jr. one week before Reagan ousted Haig and replaced him with Shultz.

Since then, Shultz has been preoccupied primarily with the Middle East crisis. While he had boned up on U.S.-Soviet relations in the past few days, U.S. sources acknowledge that the secretary regarded the meeting today largely as the start of a feeling-out process on which to build future approaches to Moscow.

As is customary, the two meetings will cover the entire range of global issues. According to the senior official, those topics that were given particular emphasis today involved arms control and a reiteration by Shultz of American insistence that the Soviets ease the repression of last December's military crackdown in Poland.

Reagan's priority emphasis on that goal has led to a major dispute with America's European allies over the sanctions imposed by Washington against European firms supplying equipment for the trans-Siberian pipeline, which will carry Soviet natural gas to Western Europe.

The U.S. aim is to use the pipeline issue as a lever to pressure the Soviets into greater flexibility toward Poland. The dominant view in diplomatic circles, however, is that Moscow, determined to stifle reform in Poland and aware of the dissension that the U.S. policy has stirred within the Atlantic alliance, has little incentive to be accommodating.

In addition, the senior official said, Shultz put special stress on human rights questions and gave Gromyko a list of Soviet dissidents whose plight the United States would like to see eased. The official declined to identify the persons on the list.

Another topic today involved Central America, where the administration previously had charged that the Soviets, working through Cuba, were actively aiding leftist guerrilla movements.

However, that was a position largely associated with Haig. Shultz has decreed that the United States take a less confrontational approach on Central American questions, and U.S. officials had predicted that Central America was unlikely to be a major factor in today's meeting.