Responding to a request from the State Department, the Civil Aeronautics Board cut back yesterday on the number of flights the Soviet state-owned airline Aeroflot is permitted to operate to and from the United States.

The action, one of many steps taken by the United States government in retaliation for the Soviet invasion of Afghanistan, reduces the number of weekly round-trip flights between Moscow and the United States from three to two beginning Sunday.

Aeroflot has the authority to operate two weekly round-trip flights to the United States -- either to New York or Washington -- under a 1974 permit issued by the CAB and approved by the president.

In recent years, however, extra flights had been authorized by an exchange of diplomatic notes between the two governments that expired last year or by exemptions granted by the CAB. This allowed Aeroflot to operate three flights weekly in the winter season (November through March) and four flights weekly the rest of the year.

Yesterday's CAB action reduces the number of flights that Aeroflot can operate to the minimum authorized in its permit.

The State Department told the CAB it had conducted a careful review of of U.S.-U.S.S.R. bilateral relations and "taking overall foreign policy considerations into account," had determined that it was "in the national interest" to reduce the number of Aeroflot's scheduled flights until further notice.

In responding favorably, the board noted that it is required to consider among other things, "the present and future needs of the foreign and domestic commerce . . . and of the national defense" in determining whether foreign air transportation is in the public interest. In light of State's request and in the absence of any other overriding considerations, the board said it found revocation of the special authority granted Aeroflot in the public interest.

The board's action could seriously affect travel to and from the 1980 Olympics. The Soviet Union has an application pending at the CAB for an extension of its exemption authority through this summer to accommodate the expected increase in traffic for the Olympic Games in Moscow. More passenger traffic than can be accommodated on connecting flights through other countries is forecast.

The Soviets already had run into some trouble from the CAB about its exemptions. In November, the CAB extended only through March 31 Aeroflot's exemption authority to run extra flights, warning that the airline's flights would be limited to two a week unless U.S. airlines were given a chance to carry passengers to the Soviet Union for the Olympics.American carriers wishing to operate charters to Moscow for the games had been encountering administrative problems getting clearances in the Soviet Union, government sources said at the time.