The Soviet KGB may have faked a tape recording of a telephone conversation between President Reagan and British Prime Minister Margaret Thatcher, the State Department said yesterday.

The tape was received by the U.S. Embassy in Amsterdam late in May about a week before the British parliamentary elections. The purported conversation dealt with last year's Falklands war and the stationing of cruise missiles in Britain.

"We checked with the White House, which advised that no such conversation took place," the State Department said in a statement.

A technical analysis of the tape, which the department said was "of poor quality," revealed that the voices were those of Reagan and Thatcher, and that the president's part of the dialogue appeared to be patched together from a November, 1982, speech on nuclear disarmament that was beamed to Europe.

"From the drift of the tape," the department statement said, "the evident purpose was to cause problems for Mrs. Thatcher by blaming her for the sinking of the British destroyer Sheffield and also for us by stirring trouble on the INF Intermediate-range Nuclear Forces issue."

The tape and a covering letter were sent anonymously to Dutch journalists. "Our examination of the text" of the letter "suggests that the author was not a native Dutch speaker," the statement said.

"This type of activity fits the pattern of fabrications circulated by the Soviet KGB, although usually they involve fake documents rather than tapes," the statement said.