The new Soviet leadership called for tougher action against corruption and crime today in a statement that appeared to signal a campaign to impose stricter discipline on the Soviet people.

A statement by the ruling Politburo said many Soviet citizens were deeply concerned about widespread corruption and lax habits among Soviet workers as well as about increasing crime in the streets.

The statement, carried on the front pages of the two main Soviet newspapers, Pravda and Izvestia, made no reference to dissident activities. Political dissent, however, is regarded as criminal activity and analysts expect new crackdowns on it.

The Politburo statement seemed designed to show the public that the new leadership under Communist Party leader Yuri Andropov was working in its interest. Normally, Politburo activities are shrouded in secrecy.

The statement today said that many people had written letters to the Politburo expressing their concern about the decline in economic and social discipline.

It said the Politburo has discussed letters from citizens throughout the country complaining mainly about poor management and embezzlement of state property.

The leadership, according to the statement, found the need to "step up the struggle against those who violate public order and against thefts of socialist property." The letters, it explained, demonstrated that some regional authorities were not carrying out their duties correctly.

Andropov, who spent 15 years as head of the KGB, the Soviet secret police, is reported to be aware of the scope of corruption. There has been speculation that he would use the issues of corruption and economic mismanagement in his struggle for full control over the vast party bureaucracy.

The most important appointment made since Andropov replaced Leonid Brezhnev as Soviet leader a month ago was the promotion of Gaidar Aliyev, 59, to full membership in the Politburo and to first deputy premier. Aliyev was a career KGB officer and a former leader of Soviet Azerbaijan.

Aliyev had made his reputation as an anticorruption campaigner in Azerbaijan, the Transcaucasian republic that has been notorious for its economic crimes. For example, he is said to have fired one-third of Azerbaijan's top leadership between 1971 and 1976.

Western analysts here believe Aliyev was brought to Moscow to carry out a similar anticorruption drive on a national scale.

While the Politburo statement today tended to reinforce the impression that the new leadership was determined to impose greater internal discipline, it also appeared to suggest a greater role for the KGB.