UPDATED 4.41pm: More details have been released about the lone gunman who shot dead four marines at two military centres in Tennessee.

The FBI is leading the investigation into the fatal shooting in Chattanooga involving Muhammad Youssef Abdulazeez, who is also dead.

US correspondent Steve Merczynski said questions are already being asked about what may have influenced him.

CNN's Alexandra Field said the shooting is being treated as an incident of domestic terrorism because the gunman targeted two military centres, although they weren't secure bases.

She said he "first went to a recruitment centre, where he opened fire."

"We've seen dozens of bullet holes in the glass windows and doors of the facility."

He then drove several miles to the second location with police in pursuit. It was here that the attack turned deadly.

The gunman has been identified as Muhammad Youssef Abdulazeez.

FBI special agent Ed Reinhold said he wasn't on the radar.

"We are looking at every possible angle. Whether it was terrorism, whether it's domestic, international or whether it was a simple criminal act."

There was a heightened state of alert owing to this being the final day of Ramadan.