The Soviet Union greeted President Reagan's reelection today with a call for improved relations between the two superpowers for the sake of world peace.

In a congratulatory cable to Reagan, the Soviet leadership expressed the hope that "the coming years will be marked by a turn for the better in relations between our countries. This would be in the interests of both our peoples and the cause of world peace."

The cable, sent in the name of the Presidium of the Supreme Soviet, said, "The Soviet Union is prepared for joint work to rectify Soviet-American relations on the basis of equality and respect for the legitimate interests of each other to remove the threat of war and radically improve the international situation."

A commentary issued by the government news agency Tass noted that Reagan, during his campaign for reelection, "was busy assuring Americans of his desire to work for a more stable peace and better relations with the Soviet Union." The main question now, Tass said, "is whether the new administration will act in keeping with its own promises. Will it back them up by deeds? The near future will show."

The Soviet Union has advanced an agenda which provides "an opportunity to look for joint realistic approaches to matters of war and peace" and primarily the need to "lessen the threat of a nuclear war," Tass said.

"There are many problems and they are complex. However, experience shows that if there is a positive, constructive approach to them, their solution is quite possible on the basis of equality and equal security, the more so as such a solution would equally accord not only with the interests of the Soviet Union and the United States but with those of the entire world as well."

Reagan's victory in yesterday's balloting was expected here. Even before any results were available, Foreign Minister Andrei Gromyko made it clear yesterday that he assumed Reagan would be returned to office.

Speaking at a Kremlin rally, Gromyko referred to recent statements by Reagan and Secretary of State George P. Shultz about the need for a "more constructive" relationship between the two superpowers. Washington's "practical actions," Gromyko added, will demonstrate whether these statements are "credible." The Soviet foreign minister also sought to assure Washington "most definitely" that the Soviet Union was prepared to "cooperate" with the United States "in the interest of strengthening international security."

Today's Tass commentary and an article on Soviet-American relations published yesterday in the daily Sovyetskaya Rosiya suggested some mild optimism here about Reagan's second term. Tass noted that four years ago Reagan campaigned for the presidency "under openly chauvinistic, militarist and anti-Soviet slogans" while this year he emphasized his desire for peace and an improvement in Soviet-American relations. The commentary ascribed the change to a "mounting anxiety" among large sections of the American population about "the growing threat of nuclear war."

It also said that the Republican Party "shamelessly" exploited a cyclical upswing in the U.S. economy. But, it said, the huge budget deficits, the mounting federal debt, high unemployment rates and an increase in the numbers of Americans living below the poverty line are all long-term problems "fraught with ruinous consequences" for the economy.

The Sovyetskaya Rosiya commentary, written by Radomir Bogadnov, deputy head of the Kremlin's think tank on American affairs, focused on Reagan's campaign rhetoric as reflecting a reassessment of the foreign and domestic policies of his first administration.

"One should only hope," Bogdanov wrote, that Reagan and his advisers will "objectively assess the consequences" of their policies to make the necessary "corrective" moves.

The confrontation approach and the quest for military superiority are bound to fail, he continued. "What is needed is a different policy, a different approach, first of all with respect to Soviet-American relations." There can be no doubt, the commentary concluded, that the American leadership will have to take into account "the realities of contemporary world." The Soviet media gave extensive and detailed coverage to the U.S. elections.