The highly publicized fight against corruption, which has become the hallmark of Soviet leader Yuri Andropov's domestic policies, was expanded to the nation's law enforcement establishment today as the new minister of interior publicly acknowledged "grave violations" of legal norms by police in the city of Odessa.

In an unusual letter published on the front page of a weekly newspaper, Army Gen. Vitaly Fedorchuk, the minister, acknowledged that a young merchant marine school student was arrested on fabricated charges and held for 20 months in jail. The student had complained about apparent corruption at the school.

Fedorchuk reported that several senior police officers in Odessa have been dismissed or disciplined for their roles in the persecution of the youth, which involved "grave violations of socialist legality."

The general, who replaced Andropov as head of the KGB secret police last May and who was promoted to head the Ministry of Interior last December, said he was taking measures to improve the work of the police.

The 63-year-old career KGB officer presumably was given control over the nation's uniformed police, criminal investigation and riot-control troops to clean up the corrupt practices for which the ministry is known.

His letter was published a day after the daily Sovietskaya Rossiya reported that senior police officers in the Krasnodaskaya region, east of Odessa, were involved in huge corruption schemes, accepting bribes in the range of 25,000 rubles (about $35,000) from various local operators and entrepreneurs.

Fedorchuk's letter apparently was designed to dramatize the struggle against corruption within the ranks of the police.

The case illuminates the arbitrariness of police and other officials.

The merchant marine school cadet, Nikolai Rozovaykin, was expelled from the school when he complained about apparent corrupt practices of its administrators and the disappearance of a relatively small sum of money earned by the cadets.

Rozovaykin subsequently was refused work in Odessa. When he complained to the authorities, he was arrested and held for 20 months on a fabricated charge of hooliganism. Eventually acquitted for lack of evidence, he was forced to work as a sweeper in the Odessa docks.

The weekly newspaper Literaturnaya Gazeta, which learned about the case last January, sent its reporters to investigate. A story published Jan. 19 provided details of how Rozovazkin, once a Young Communist League leader, was systematically persecuted for five years by influential officials in Odessa with the help of senior officers of the police and its investigative branch.

The article was published in the middle of an anticorruption drive during which police and deputized vigilantes carried out daytime raids in various public places looking for loafers and absentee workers. The nationwide campaign generated bitterness against the police, who are said to be corrupt, particularly in provincial cities and towns.

Literaturnaya Gazeta said it has received about 2,000 letters to the editor in response to its account of Rozovaykin's predicament. Apparently the letters were sharply critical of police activities generally.

Observers here interpreted Fedorchuk's front page letter in Literaturnaya Gazeta as an attempt to demonstrate an intent to extend the anticorruption campaign to the uniformed police force itself.