BOSTON — A knife-wielding man killed by terror investigators had planned to behead an unidentified victim, then changed his mind and said he wanted to kill police officers, the FBI said.

Usaama Rahim plotted for at least a week, the FBI said in a complaint against a family member who was arrested Tuesday, hours after Rahim was shot to death. The relative, David Wright, was ordered held Wednesday on a charge of conspiracy with intent to obstruct a federal investigation.

The FBI said Rahim bought three fighting knives and a sharpener on or before May 26. On Tuesday, he told Wright he planned to begin trying to randomly kill police officers, the FBI said.

An anti-terror task force of FBI agents and Boston police, faced with an imminent threat, confronted Rahim on a sidewalk and fatally shot him when he refused to drop his knife, authorities said.

Rahim and Wright were heard in a recorded conversation talking about “thinking with your head on your chest,” a reference to Islamic State propaganda videos showing severed heads on the chests of beheading victims, the FBI said in an affidavit written by an agent assigned to Boston’s Joint Terrorism Task Force.

Rahim initially told Wright about a plan to behead an unidentified victim outside Massachusetts, and on Sunday, Rahim, Wright and an unidentified man met on a beach in Rhode Island to “discuss their plans,” the FBI affidavit said.

“Wright indicated that he agreed with Rahim’s plan and supported it,” the affidavit states.

Authorities searched a home in Warwick, Rhode Island, on Tuesday and Wednesday but wouldn’t confirm the search was related to the investigation.