Imran Ali Rasheed, 32, "may have been inspired by a foreign terrorist organization to commit these crimes," an FBI official said during a joint press conference with the Garland and Plano police departments.
Police investigators and the FBI are working to determine if Sunday's attack should be classified as an "act of terrorism."
Dallas FBI Special Agent in Charge Matthew De Sarno made clear that "inspired by" an organization does not mean Rasheed was directed by an outside group.
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“What inspired means is we’ve not found indication that Rasheed was either directed by or in contact with foreign terrorist organization actors,” De Sarno said. “We believe, at this point, that he was inspired by rhetoric or propaganda by foreign terrorist organizations.”
De Sarno would not specify what terrorist group may have inspired Rasheed.
The local police departments said they notified the FBI when they discovered a note Rasheed left in his victim's vehicle, but De Sarno did not go into details about a potential motive in either incident.
Police said they believe Rasheed acted alone.
Police said the first shooting happened Sunday, just before 12 p.m. in the 400 block of Forest Gate Drive in Garland.
Authorities identified the Lyft driver Monday as 26-year-old Isabella Ann Lewis. There was no indication Lewis and Rasheed knew each other, just that she picked him up for a Lyft ride, Garland police Chief Jeff Bryan said.
Bryan said Lewis picked up Rasheed and he fatally shot her during the car ride. Rasheed then pulled her body out of her car and took off in it, Bryan added.
Lewis' car was later located outside the Plano Police Department, where authorities said a gunman, identified Monday as Rasheed, fired a handgun at a civilian police employee and a citizen in the lobby.
Rasheed initially went into the lobby telling the civilian police employee that there was a man was outside in the parking lot acting weird. As the employee called for police to respond, Rasheed is accused of returning to the lobby with a mask on, a semi-automatic pistol and opening fire.
Plano police Chief Ed Drain said an officer ran out and fired three rounds, all of which struck Rasheed. He was taken to a local hospital and later died.
Because an officer was involved in the shooting, Drain said the department was conducting a review with the Collin County District Attorney's Office.
He added that Rasheed was not a Plano resident and did not know why he targeted the city's police department. Officers had no previous contact with Rasheed, Drain added
Rasheed was on the FBI's radar eight years ago, De Sarno said, but a counterterrorism operation conducted from 2010-13 determined that Rasheed "did not pose a threat." The case was then closed.
De Sarno said the investigation was thoroughly reviewed Sunday and he was confident it was done "thoroughly and properly."
De Sarno would not say if Rasheed's home had been searched or if police found additional weapons on Rasheed or in the vehicle.
The Plano Police Department headquarters' lobby will remain closed until Wednesday, Drain said.
The FBI asked anyone with relevant information about Rasheed or Sunday's incident to submit it at tips.fbi.gov or by calling 1-800-CALL-FBI.