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. They also wouldn’t confirm how Rahim, 26, and Wright, 24, are related.

Early Tuesday morning, Rahim called Wright and told him he had changed his plans and no longer planned to kill someone in another state, the affidavit says. Instead, he said he was going to "go after" the "boys in blue," it says, an apparent reference to police officers.

During the recorded conversation, Rahim told Wright, "Yeah, I’m going to be on vacation right here in Massachusetts. … I’m just going to, ah, go after them, those boys in blue," the affidavit says.

The FBI said the phrase "going on vacation" refers to committing violent jihad.

Authorities allege that during that conversation, Wright advised Rahim to destroy his smartphone, wipe his laptop computer and prepare his will.

On Wednesday, authorities moved swiftly to manage perceptions of the shooting, which killed a black man whose family is well known among Muslims and African-Americans in Boston.

Rahim’s mother is a nurse at Boston University. His older brother, Ibrahim Rahim, is a scholar known for preaching after the Boston marathon bombings that violence is anti-Islamic.

Ibrahim Rahim initially posted a message on Facebook alleging police repeatedly shot his brother in the back while he was on a cellphone calling their father for help. But his version unraveled Wednesday after police showed their video of the confrontation to community leaders.

Darnell Williams, president of the Urban League of Eastern Massachusetts, said he could "150 percent corroborate" the police account. The images clearly show that Usaama Rahim "was not on a cellphone and was not shot in the back," Williams said.

Police Commissioner William Evans said officers confronted Rahim because "military and law enforcement lives were at threat."

The video, which police did not make available publicly, shows that Rahim menaced the officers with a large military-style knife and they initially backed away before shooting him when he refused to drop it, police said.

Williams said he’s not ready to call the shooting justifiable, and a Boston Muslim leader, Imam Abdullah Faaruuq, said it was unclear from the "inconclusive" video whether police had to use deadly force.

"They might have approached him in a different way," Faaruuq said.

Ibrahim Rahim could not be reached for comment Wednesday as he traveled to Boston to bury his brother.

Usaama Rahim was under investigation after spreading Islamic State propaganda online and communicating with other people about it, said U.S. Rep. Michael McCaul, who chairs the House Homeland Security Committee.

"These cases are a reminder of the dangers posed by individuals radicalized through social media," the Texas Republican said.

Prosecutor Stephanie Siegmann said Wright posed a serious risk of fleeing or obstructing justice if not held pending a June 19 hearing. Wright’s attorney, Jessica Hedges, denied that, saying he has deep roots in the Boston area and an "incredibly loving and supportive family."

Hedges urged the government to be "as transparent as possible" and "abide by the law" as it investigates this case, saying "we have serious concerns about that already."

Boston voter registration records describe Usaama Rahim as a student. A spokeswoman said Rahim had worked for CVS since March.