TV newswoman Lee Carter (Paula Prentiss) is one of many witnesses to the public assassination of presidential candidate Senator Charles Carroll (Bill Joyce) atop the Seattle Space Needle. A waiter armed with a revolver is chased but falls to his death. Meanwhile, a second waiter, also armed, leaves the crime scene unnoticed. A Congressional special committee determines that the assassination was the work of a lone gunman.
Three years later, Carter visits her former boyfriend and colleague, newspaper reporter Joe Frady (Warren Beatty). Lee tells Frady that she feels there is more to the assassination than was reported at the time. Six of the witnesses to Carroll's assassination have since died, so she fears she will be next. Frady does not take her seriously. Carter is soon found dead and her death is judged by the police to be either a voluntary or accidental drug overdose.
Investigating Carter's leads, Frady goes to the small town of Salmontail whose sheriff, L.D. Wicker (Kelly Thordsen), attempts to trap him below a dam while the floodgates are opening. Frady narrowly escapes but the sheriff drowns. Frady finds information about the Parallax Corporation in the sheriff's house and learns that its real business is recruiting political assassins.
As Frady is interviewing Carroll's former aide Austin Tucker (William Daniels) aboard Tucker's boat, a bomb explodes. Frady survives but is believed dead. He decides to apply to Parallax under an assumed identity. Jack Younger (Walter McGinn), a Parallax official, assures Frady that he is the kind of man they are interested in. Frady is accepted for training in Los Angeles, where he watches a slide show that conflates positive images with negative actions.
Frady recognizes a Parallax man from a photo Tucker showed him: the Parallax Assassin was a waiter in the Space Needle restaurant the day Senator Carroll was murdered. He watches the Parallax Assassin retrieve a bag from a car, then drive to an airport and check it as baggage on a plane (a Globe Airlines Boeing 707 jetliner). Frady boards the plane. He notices a Senator aboard, but not the Parallax man, who is on the airport's roof watching the plane take off. Frady writes a warning to the effect of "There is a bomb on this plane" on a napkin and slips it onto the drink service cart. The warning is found and the plane returns to Los Angeles. Passengers are evacuated moments before a bomb explodes.
Frady's generally skeptical editor Bill Rintels (Hume Cronyn) listens to a secretly recorded tape of a conversation Frady had with Jack Younger. Rintels places it in an envelope, apparently with other such tapes. A disguised Parallax assassin delivers coffee and food to Rintels' office. Rintels is poisoned and the tapes disappear.
Frady follows the Parallax associates to the dress rehearsal for a political rally for Senator George Hammond (Jim Davis). Frady hides in the auditorium's rafters to secretly observe the Parallax men, who are posing as security personnel. Frady realizes too late he has been set up as a scapegoat. Hammond is shot dead by an unseen gunman. As Frady is trying to escape, he is seen in the rafters and a Parallax agent kills Frady with a shotgun.
The same committee that determined a lone gunman killed Senator Carroll now reports that Frady, acting alone, killed Senator Hammond out of a misguided sense of patriotism and a paranoid belief that the Senator was trying to kill him. The committee further expresses the hope that their verdict will end political assassination conspiracy theories. They do not take questions from the press.