Washington — Washington is guardedly encouraged by the sounds of moderation coming from the Kremlin. The events in Moscow of the past couple of days, played out to the solemn backdrop of the state funeral for Yuri Andropov, show that both superpowers are at least speaking to each other in more conciliatory terms.
Both sides now appear to be gingerly feeling each other out about the possibilities of a relaxation in tensions. The atmosphere has improved a notch.
The big question, diplomatic analysts say, is whether the two sides can really come to grips with the substantive issues dividing them - above all, the knotty problem of arms control.
Washington does not yet see any substantive shift of Soviet policy - even though Vice-President George Bush, after meeting briefly with the new Soviet leader, Konstantin Chernenko, in Moscow on Tuesday, said that ''the spirit of the meeting was excellent.''
Mr. Bush said Mr. Chernenko ''agrees about the need to place our relationship upon a more constructive path.''
But the US vice-president, who also delivered a letter to Chernenko from President Reagan, added that ''progress will not be easy or quick.''
Similarly, Reagan officials caution against reading too much into the Soviet leader's acceptance speech to the Communist Party's Central Committee on Monday.
These officials do note that although Chernenko took a jab at ''some leaders of the capitalist countries,'' he did not specifically attack the United States by name or the American President personally. Also, while he voiced the usual Soviet line about not letting the military equilibrium be upset and assailed the ''reckless, adventurist actions of imperialism's aggressive forces,'' he struck a conciliatory tone in these words:
''We are for a peaceful settlement of all disputable international problems through serious, equal, and constructive talks. The USSR will cooperate in full measures with all states which are prepared to assist through practical deeds to lessening international tensions and creating an atmosphere of trust in the world.''
This suggests to diplomatic experts that the Soviet leadership may use the chance afforded by a change on the Politburo to try to find a way to reduce the tensions that have gripped relations since the downing of the Korean airliner last fall.
''There was no great gesture in the Chernenko speech,'' a State Department official comments. ''But there was a fair amount of care not to get into strong rhetoric, to take a middle ground.''
Significance is also attached to the fact that Chernenko did not play up the Soviet military establishment. ''His pledge to the military was no more than it had to be,'' says a department specialist on the Soviet Union.
In recent weeks, President Reagan also has toned down his public rhetoric and is probing for any Soviet flexibility.
Some administration analysts are intrigued by the eulogy to Mr. Andropov delivered by Soviet Foreign Minister Andrei Gromyko. Mr. Gromyko spoke of Andropov's personal involvement in foreign affairs, suggesting he may be giving the new Kremlin leadership the option of distancing itself from the Andropov era. Other specialists, however, see an early thread of consistency and continuity in Soviet policies both at home and abroad.
Mr. Gromyko is expected to continue to play an influential role on the Politburo within the context of a stronger collective leadership. In light of Chernenko's inexperience in foreign affairs, he is likely to depend heavily on Gromyko and other ''pros,'' say US officials. But it is not ruled out that the new Communist Party general secretary will develop as a leader.
Chernenko, although strongly identified with Leonid Brezhnev's policy of detente, has had only limited exposure to the West. In the late 1960s he paid an unobtrusive visit to the US to learn about computers and data processing. He accompanied Mr. Brezhnev to the Helsinki conference on European security in 1975 , and he was in Vienna in 1979 at the time of the signing of the SALT II agreement.
US officials note that with the elevation of Chernenko, a party bureaucrat, to be secretary general, the Soviet Communist Party has redressed the internal balance and is back in first place. Andropov had come out of the KGB and also had the strong support of the military.