Elton Simpson has been identified as one of the suspected gunmen who attacked an event in the Dallas suburb of Garland on cartoons of the Prophet Muhammad.
Elton Simpson had been previously investigated on suspicion of terrorism offences, the FBI said.
Agents were searching an apartment in Phoenix, Arizona, where Elton Simpson reportedly lived, an FBI official said.
Two gunmen were shot dead after opening fire outside Sunday’s event.
They drove to the Muhammad Art Exhibit in the Dallas suburb of Garland as the event was ending, firing with assault rifles on two officers in a parking lot.
One of the officers, a traffic policeman, returned fire and killed both the gunmen, Garland police official Joe Harn said. The security officer was also shot in the lower leg. He was treated in hospital and then released.
“Obviously they were there to shoot people,” Joe Harn said.
The event was organized by the American Freedom Defense Initiative (AFDI), which is run by controversial blogger and activist Pamela Geller.
One of the keynote speakers was the Dutch politician Geert Wilders, an outspoken critic of Islam in Western societies.
The conference included a contest that offered a $10,000 prize for a cartoon of the Prophet Muhammad. Depictions of the Prophet Muhammad are offensive to many Muslims.
Officials believe that Elton Simpson sent several Twitter messages before the Sunday’s shooting, including one with the hashtag #texasattack part of which read: “May Allah accept us as mujahideen [holy fighters].”
The Twitter account was later suspended.
Elton Simpson was convicted several years ago for lying to authorities about his plans to travel to Somalia, court documents show.
The bomb squad was called in to search the suspects’ vehicle. They set off several controlled explosions around the vehicle, where they found additional ammunition but no bombs, Joe Harn said.
He would not confirm the identity of the suspects, though he said officials believed they knew who the gunmen were.
The suspects’ bodies remained at the scene on Monday morning, surrounded by dozens of empty shell casings.
Security had been tight ahead of Sunday’s conference and Garland’s mayor acknowledged that there had been a lot of local concern about the event, though police said there had been no credible threats.
A security plan had been put in place over several months, and event organizers paid $10,000 for additional security on the advice of the police, Joe Harn said.
Pamela Geller said she was standing up for free speech, adding: “This terrible incident reflects the need for such conferences.”
“We are continually abridging our freedoms so as not to offend savages,” she said.
Pamela Geller denied she was anti-Muslim, only “anti-jihad”.