Soviet leader Yuri Andropov called for an improvement in Soviet-American relations today and asserted that "the Soviet Union is ready and interested to search for joint initiatives which would make the present situation easier."

In his second meeting with an American since he took office last November, Andropov expressed concern about the state of bilateral relations and said Reagan administration policies have created a situation "which cannot but give rise to alarm."

But Andropov told W. Averell Harriman, the veteran diplomat who served as ambassador here during World War II, that the Soviet Union was seeking to develop "balanced, mutually beneficial, and which is even better, good-neighborly relations with the United States."

Speaking to journalists after their 80-minute meeting, Harriman said he was "authorized" to say that "it is the most sincere and fervent desire of the Soviet government to have normal relations with the United States and to develop them in the best traditions of our relations in the past."

The 91-year-old Harriman quoted Andropov as referring to "good traditions" during World War II when "our countries were allies." A Soviet account of the meeting said Andropov saw "the threat of war" as a new "common enemy" of the two countries.

Harriman said he found the 68-year-old Andropov in apparently good health. He described Andropov as "vigorous" and said their discussion was "clear and intelligent."

"I was impressed by his grasp of issues," Harriman added.

The former New York governor said Andropov was "cordial, agreeable, very blunt and frank and straightforward."

The conciliatory tone of Andropov's remarks today was yet another in a series of mixed signals from Moscow. Recent Soviet pronouncements have alternated between grave threats and hints of compromise.

Harriman, who insisted that he traveled here as a private citizen, refused to disclose the substance of the talks.

The meeting, Harriman said, "gave me an opportunity to understand the Soviet point of view, and I think this would be useful when I talk to people in and out of the government" in Washington. Harriman had met with Secretary of State George P. Shultz and other officials before coming to Moscow.

Observers here said Andropov may have been using the diplomat with long personal, professional and even emotional ties to Moscow in an effort to reestablish a dialogue with Washington before the two superpowers reach a crisis when new U.S. missiles are due to be deployed in Western Europe.

Harriman's ties to this country date to 1899, when as a boy he accompanied his father on a Russian hunting trip. The Harrimans had extensive financial interests in Russia, and Harriman has known every Soviet leader since Stalin.

Andropov's only other meeting with Americans was on the day of his predecessor Leonid Brezhnev's funeral, when the new leader spent 30 minutes with Shultz and Vice President Bush. That session generated unfulfilled expectations hopes that it would lead to a halt in the steady deterioration of Soviet-U.S. ties.

Today's meeting in Andropov's office at the Central Committee building appeared to have been more relaxed. Harriman was accompanied by his wife, Pamela, and by Peter Swiers, a State Department official who traveled with the Harrimans here. Also present was Andrei Alexandrov Agentov, Andropov's foreign policy adviser.

The government news agency Tass quoted Andropov as saying that the awareness of a risk of nuclear holocaust "should become the common denominator inducing" both Soviet and American leaders "to display reciprocal restraint." This, Tass said, could become "a basis for the concentrated effort to find mutually acceptable accords to prevent what cannot be remedied."

Andropov said that "unfortunately" the Reagan administration has not adopted "such a responsible approach" and that it is seeking to acquire military superiority over the Soviet Union.

"We are convinced," Andropov said, "that in the present-day international conditions, taking into consideration the overall strategic situation and the growing number of explosive problems in the world, the Soviet Union and the United States cannot allow themselves to be oriented at military competition."

Tass quoted Harriman as expressing his concern over the current state of relations and "speaking in favor of their normalization."

It was not clear what Andropov had in mind when he talked of Moscow's interest in " joint initiatives."

There was speculation here that apart from the issues of nuclear weapons, the two men may have discussed the situation in the Middle East, Afghanistan, Central America and other troublesome problems.

One indication that these issues may have been involved was the fact that U.S. Ambassador Arthur Hartman requested a meeting with Foreign Minister Andrei Gromyko two days ago and the two men were reported to have discussed Afghanistan and the Middle East.

According to a senior western diplomat, Hartman had expressed U.S. concern about the Syrian military buildup in Lebanon, and particularly about an attack by Syrian planes on Israeli aircraft over Lebanon. According to the diplomat, the United States had cautioned Moscow about dangers involved in Syria's military activities in Lebanon.

While not mentioning details, Harriman said he told Andropov that the Soviet Union could take some unspecified steps to ease international tension. "We should work on some solvable problems," Harriman said, suggesting that this was one of the ways to "bring the two governments together."