The young man who killed four US Marines in Tennessee in the latest shooting rampage in America had not given authorities any reason to keep him under surveillance, the mayor said Friday.

Chattanooga mayor Andy Berke spoke as federal and other authorities scrambled to try to determine a motive for Thursday's shootings.

The gunman, who died in the shootings at two US military facilities, has been identified as 24-year-old Mohammod Youssuf Abdulazeez, who was allegedly born in Kuwait.

Media reports described him however as having had a traditional American upbringing, including participation on school sports teams.

Berke, speaking on CNN early Friday, was asked whether the man had been on "the radar" of local authorities.

"He was not, as far as we know," Berke answered.

He added: "Much of that information that involves terrorism we get from the federal government. We certainly didn't have any indication that he was a threat or that yesterday something was going to happen."

Berke said investigators at all levels are examining any and all connections the shooter may have had.

"Obviously the local component is important, but I can also tell you that law enforcement is not solely focused on the local part. They are examining what his connections were anywhere and everywhere," the mayor said.