Soviet Prime Minister Nikolai Tikhonov tonight welcomed President Reagan's stated intention to improve relations with the Soviet Union. The new Kremlin leadership, Tikhonov said, was in favor of "normal, or even better, friendly relations with the United States."

Hosting a Kremlin dinner for more than 250 U.S. business executives, Tikhonov said a decline in political relations has led to a sharp drop in bilateral trade.

His address, however, was unusually warm and it skirted most basic issues that have brought Soviet-American relations to their lowest point in years.

The Soviets were given a detailed, official U.S. account of export-control revisions today and many American businessmen said later that they felt the atmosphere already had improved considerably. Sen. Robert Dole (R-Kan.), who led a congressional delegation that attended the council meetings, said, "It is still cloudy but the storm has passed."

Diplomatic analysts interpreted Tikhonov's remarks as a signal that the Soviets are trying to scale down the rhetoric while awaiting Reagan's next move.

It was the first pronouncement on Soviet-American relations by a senior figure since Yuri Andropov replaced Leonid Brezhnev last Friday as the leader of the Soviet Communist Party. Brezhnev died from a heart attack at age 75 on Nov. 10.

The official news agency Tass, which published the speech, said Tikhonov was speaking "on behalf of the leadership."

"President Ronald Reagan has recently declared the wish of the United States to work in the direction of improving relations with the Soviet Union and expanding the field where our countries can cooperate with each other for mutual benefit," Tikhonov said.

"I can say that this fully accords with the Soviet Union's wishes and intentions."

The speech capped three days of meetings of the Soviet-American Trade Council and a series of blunt Soviet signals that Moscow expects some concrete evidence of changes in Reagan's policy before it would join him in a search for "a more constructive relationship."

It was understood that Tikhonov, during a private session earlier today with William Varity, chairman of Armco Inc. and cochairman of the council, had raised the question of what he saw as unyielding U.S. positions at the two sets of Soviet-American arms negotiations in Geneva. The issue of arms control is central to relations between the superpowers.

Six senior U.S. executives were briefed extensively, before Brezhnev's death, by Secretary of State George P. Shultz and Commerce Secretary Malcolm Baldrige in an effort to revive Soviet-American trade, well-informed sources said. The death of Brezhnev and Reagan's conciliatory gestures, including the lifting of the Siberian gas pipeline sanctions, have introduced a new atmosphere in which the visit by U.S. businessmen acquired added significance.

Although the U.S. Embassy has maintained that the visit of the American executives was not encouraged by the Reagan administration, the sources said that the senior American members of the council were encouraged by Shultz in June to attend the meeeting here this week.

The visiting Americans were subjected to an apparently carefully prepared effort to outline fundamental Soviet concerns. Observers here suggested that the intention of the Soviets, who believe in the power of corporate America, may have been to have businessmen, eager to rebuild trade, also exert political influence on the Republican administration.

Among prominent business leaders were the chairmen of such companies as Tenneco Inc., Dresser Industries Inc., Allis-Chalmers Corp., Abbott Laboratories, Dow Chemical Co., Cargill Inc., International Harvester Co., Stauffer Chemical Co., FMC Corp., and many others.

First, Foreign Trade Minister Nikolai Patolichev told the council that Washington would have to "renounce once and for all" the use of trade as a political tool before Soviet-American commerce could be revived.

Then, First Deputy Foreign Minister Georgy Kornienko attacked the Reagan administration's arms control and human rights policies. Yesterday, the Kremlin's top expert on U.S. affairs, Georgy Arbatov, stressed the same concerns.

Tikhonov today took the high road, avoiding all divisive issues except trade, to create a distinctly positive impression on his audience.

"All sorts of discriminatory measures, attempts to use various so-called sanctions, embargos, etc. against our country do not, as a matter of course, inspire kind feelings but rather undermine the confidence of Soviet foreign trade organizations in the American market," Tikhonov said. "Under such conditions it is hard to expect a substantial growth in trade, whatever commodities may be in question. I am saying that quite frankly, as I wish that there be absolute clarity on that issue."

He said the Soviet Union wants to trade "on an equal footing." He continued, "If we speak of Soviet-American relations, interest in that case is no less political, because healthy trade strengthens the basis for peaceful, good-neighborly relations, which are highly important for the international situation as a whole."

He again underlined Moscow's expressed desire to have good relations with Washington. "There were such relations in the past and they can again become a reality," he said. "This would meet the interests of our two countries and the interests of world peace."