The recent bitter public exchanges between President Reagan and Soviet leader Yuri Andropov appear to foreshadow a new crisis in Soviet-U.S. relations and the possible advent of a second Cold War.

This is the view of Soviet and foreign political observers in Moscow following Reagan's March 8 attack on Moscow as an "evil empire" and his March 23 proposal to shift the U.S. posture to base nuclear deterrence on a new antiballistic missile system.

Even discounting rhetoric, the Russians seem to have decided that meaningful arms control talks are becoming more elusive and that the logic of the two sides' positions makes a new round of the arms race virtually inevitable.

Such a conclusion was suggested by Andropov's March 26 response, in which he questioned not only the sincerity of Reagan's intentions but also the rationality of his basic assumptions.

The harshness of Andropov's remarks about the president is virtually without precedent since the days of the Cold War. While the Soviet media have assailed U.S. presidents in bitter and vitriolic terms, top Soviet leaders have resorted extremely rarely to direct personal attacks on American leaders.

As seen from Moscow, Reagan has rejected compromise in the already thorny dispute about the scheduled deployment of new U.S. medium-range missiles in Western Europe. The Russians have clearly indicated that the deployment of 108 Pershing II missiles in West Germany could lead to a crisis in relations that would be similar to the 1962 Cuban missile crisis. But they have at the same time let it be known that they could live with the deployment of U.S. cruise missiles--which are much slower than the Pershings and thus easier to defend against--and that they are prepared to negotiate a deal allowing one but not the other.

The Pershing is said to be unacceptable to Soviet military chiefs who regard it as a first-strike weapon capable of launching a surprise attack.

Reagan's new proposal to develop more sophisticated antiballistic missile systems including those based in space raised a qualitatively new issue. Andropov and other Soviet officials have made it clear that they would match any new U.S. weapons system.

Behind the current dispute is the essential fact that Moscow, like Washington, regards nuclear weapons not only as potential agents of catastrophic devastation but also as instruments of power and influence in the world.

In the Soviet view, the Reagan administration is intent on denying equal status of any kind to the Soviet Union by abandoning the agreements reached at the 1972 Moscow summit between president Richard Nixon and general secretary Leonid Brezhnev. At that time Nixon conceded equal status to Moscow by formally acknowledging the existence of strategic parity between the two superpowers.

The Russians now see Reagan as preparing for confrontation and applying pressure on the Soviet economy in order to weaken it and force a reduction of its military potential.

In pursuing this policy, according to this view, Reagan is exaggerating Moscow's military strength while simultaneously overemphasizing the Soviet Union's economic and internal problems. The extent to which this approach has annoyed the Russians is reflected in Andropov's remark that Reagan was resorting to techiques "inadmissible in relations between states."

Both Andropov and Brezhnev have made it clear that they were prepared to go to any length to maintain the cherished parity. As one long-time observer said after the latest Andropov statement on the subject, "The Russians are prepared to go to a nuclear confrontation and die holding the concept of parity close to their hearts."

Reagan's confrontational approach is likely to have a definite impact on internal Kremlin arguments, and there have been some curious signals in the past few days.

One was the promotion of Foreign Minister Andrei Gromyko to the post of first deputy prime minister. It is unclear why such a promotion was necessary at this time since Gromyko, as a Politburo member for the past 10 years, was already in charge of Soviet foreign relations. The other curious promotions involved four senior Soviet generals--including Soviet rocket force commander Vladimir Tolubko--who were named marshals.

Speculation here is that these steps involve greater centralization of authority for what is expected to be a serious showdown with the United States and to reflect the growing importance of the military.

In the past, whenever the Soviet leaders have seen themselves challenged to a new round of the arms race, they have responded by concentrating their efforts on a military buildup.

They did so in the 1940s, when the United States became the first to acquire atomic weapons; they did it again after their humiliating retreat in the 1962 Cuban missile crisis, which demonstrated U.S. strategic superiority and reinforced Soviet determination to catch up.

On the other hand, Kremlin leaders have opted for accommodation when it seemed fruitful. They did so after Stalin's death in 1953 and with detente in the early 1970s. Some major East-West problems were resolved in these periods including the Korean War and the status of Germany.

Since Reagan entered the White House, the Russians generally have sought to keep the level and tone of their public rhetoric less openly antagonistic than the president has. That attitude seemed to have come to an end last October when Brezhnev, under the pressure of armed forces chiefs, signaled a change in Soviet policy toward confrontation with Washington.

The death of Brezhnev and high-level, Soviet-American contacts produced an interlude of expectations here that an accommodation with the United States might be possible. Moreover, the Russians expected that this month's West German elections could produce a parliamentary majority for the Social Democrats and the Greens, thus possibly delaying the scheduled deployment of new U.S. missiles.

In retrospect, Moscow has misjudged the strength of links between the United States and Western Europe. The resounding victory of the Christian Democrats in West Germany seems to have also raised questions here about the strength of antinuclear forces in the West and their ability to influence policy.

There is another important fact. Andropov is not Brezhnev. He is not wedded to detente. Moreover, he owes his present position to a large extent to the Soviet armed forces.

The Russians would prefer not to go into another round of the expensive arms race, knowing that it would add new burdens to an already overburdened economy. In this context, Moscow has not closed the door to Reagan, since Soviet diplomacy rarely closes doors to any option. But the conviction here now seems to be that Reagan does not intend to walk through those doors.

The Russians have lost their "European option" and are increasingly uncertain about the role of antinuclear forces in the West. Given those factors, the size of Reagan's budget requests for defense and the current view here that the president is likely to be reelected, the Russians are seen as having little room for maneuver.

In such situations, the voice of the armed forces gains additional weight. Their argument is said to be that Moscow has no option but to start its own parallel rearmament program. Time is running out, and hard decisions have to be made.

The prevailing view among diplomatic observers here is that the two superpowers are already in a new round of weapons development and procurement. The Soviets have let it be known that they have successfully tested their own cruise missile and a new intercontinental ballistic missile.

According to this view, the absence of some American concessions would merely intensify the Soviet military buildup as well as the growing Cold War climate between the two superpowers.