WASHINGTON—The chairman of the Senate intelligence committee levied an extraordinary barrage of criticism against the Central Intelligence Agency, saying it may have violated the Constitution and U.S. laws by spying on a congressional review early this year.

Sen. Dianne Feinstein (D., Calif.) said in a speech from the Senate floor that the CIA had conducted improper searches of committee computers being used by staff members. The CIA director quickly rebuffed that accusation, saying a Justice Department review would show...