Four Marines and a sailor were killed in the attack -- which authorities are treating as "an act of terrorism" -- before the gunman, Mohammad Youssuf Abdulazeez, died in a shootout with police.
"There are no words to describe our shock, horror and grief," Abdulazeez's family said in a statement cited by an NPR public radio journalist.
"The person who committed this horrible crime was not the son we knew and loved," it added.
"For many years, our son suffered from depression. It grieves us beyond belief to know that his pain found its expression in this heinous act of violence."
Investigators are seeking to determine a motive behind Thursday's rampage on two military centers in Chattanooga.
The Federal Bureau of Investigation has asked foreign intelligence agencies to help trace Abdulazeez's movements and activities abroad, and analysts are monitoring his activity on social media.
A law enforcement official told the New York Times investigators were looking into a text message Abdulazeez allegedly sent to a friend hours before the shooting to probe possible motives.
The text reportedly included an Islamic verse: "Whosoever shows enmity to a friend of Mine, then I have declared war against him," according to the newspaper.
"Every one of our resources are being devoted to this investigation," Chattanooga Mayor Andy Berke told CNN.
But the FBI warned against jumping to conclusions, after Michael McCaul, chairman of the House of Representatives Homeland Security Committee, branded the assault "an ISIS-inspired attack," using an alternative acronym for the Islamic State group.
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