The Soviet Union charged yesterday that a bomb attack Thursday night on its Aeroflot Airlines office in downtown Washington was carried out "with the connivance of the American authorities," an allegation that the State Department rejected.

The blast, which occurred at 11:10 p.m. and could be heard for blocks, shattered three windows at the airline's headquarters at 16th and L streets NW, blew gaping holes in the interior walls of the office and in a wall-size photograph of Moscow's Red Square, and knocked down one of the Cyrillic letters spelling " Aeroflot" on the building's facade.

No one was in the office at the time and no one was injured.

The FBI, which is investigating the blast with the D.C. police department, said no one has claimed responsibility for the bombing, in which a pipe bomb apparently was used.

It was the fourth bombing in six years at the office where the Soviet airline continues to make reservations for foreign travel, even though President Reagan suspended Aeroflot service here early last year in retaliation for alleged Soviet involvement in the crackdown in Poland.

The last previous bombing, also believed to have been caused by a pipe bomb, came a year ago today. Minutes after that explosion, The Washington Post had received a call from a person who said, "This is the Jewish Defense League," and claimed that the explosion commemorated an anniversary connected with a Soviet woman being punished because she wanted to go to Israel.

The Soviet news agency Tass said that Thursday's bombing was "not the first" attack on "Soviet institutions and citizens" in the United States. Tass said that such "criminal provocations" were being mounted by "fascist thugs from groupings of the type of the Jewish Defense League, the anti-Cuban and other scum" who usually are not apprehended by U.S. authorities.

No suspects have been arrested in the previous bombings at the Aeroflot office.

The State Department said that it "categorically" rejects any suggestion of U.S. involvement in the explosion, and added: "The U.S. government has consistently affirmed its opposition to terrorism in any form."