Mohammad Youssuf Abdulazeez, the man who shot and killed five US troops in Tennessee suffered from depression, his family said on Saturday in condemning the "heinous act of violence."
Four Marines and a sailor were killed in the attack -- which authorities are treating as "an act of terrorism" -- before the gunman 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. 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," it said.
Expressing its condolences to the families of the victims, the Abdulazeez family also vowed to continue to cooperate with law enforcement.
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.
Abdulazeez, 24, was a naturalized US citizen born in Kuwait.
"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.
"At this time, we have no indication that he was inspired by or directed by anyone other than himself," FBI special agent Ed Reinhold said, referring to Abdulazeez.
The shooting has jarred the city of 168,000, where the Islamic Society of Greater Chattanooga condemned the attack and canceled its end-of-Ramadan Eid al-Fitr celebrations out of respect for the victims.
Going into the weekend, more details emerged about Abdulazeez, a University of Tennessee engineering graduate and mixed martial arts enthusiast who grew up in a middle-class neighborhood.
Investigators were looking at Abdulazeez's foreign travel, with a reported trip to Jordan last year of particular interest.
There was evidence that he came from a troubled family. Divorce papers filed by his mother alleged that his father beat his wife and five children.
The father was also reportedly investigated for ties to a terrorist group, but ultimately was cleared.
Abdulazeez's only known brush with the law was in April, when he was arrested for driving under the influence.
He briefly worked at a nuclear power plant in Ohio in May 2013, but was fired after failing to meet minimum employment requirements, a spokeswoman for Perry Nuclear Power Plant operator FirstEnergy said.
In Washington, Defense Secretary Ashton Carter has asked for recommendations on how to boost security for troops and civilians at military installations.
But state governors in Arkansas, Florida, Indiana, Louisiana, Oklahoma and Texas signed executive orders that would allow US military personnel to carry firearms at recruiting centers.
Such facilities are often located in shopping malls, with no special security measures and recruiting staff inside unarmed.
"After the recent shooting in Chattanooga, it has become clear that our military personnel must have the ability to defend themselves against these type of attacks on our own soil," Texas Governor Greg Abbott said.
Republican Senator Ron Johnson, who chairs the Senate Homeland Security Committee, said he would introduce a bill ending the ban on troops carrying certain firearms on military installations.
Utah, which last year passed legislation allowing soldiers at National Guard facilities to carry weapons, said it would "explore additional ways to protect our men and women serving in the Armed Forces" in the wake of the attack, according to a statement from Governor Gary Herbert.
Republican presidential hopefuls Jeb Bush, Donald Trump and Scott Walker called for the lifting of a prohibition on military personnel carrying firearms at recruiting venues.
The four Marines died Thursday, while the fifth victims, a sailor, succumbed on Saturday to injuries he sustained in the assault.
The Navy named the sailor as Logistics Specialist 2nd Class Randall Smith, a father of three daughters who had recently re-enlisted and transferred to Chattanooga.
"It's hard to understand how somebody can hurt somebody that's serving for you, for your freedom, for your safety," his step-grandmother Darlene Proxmire told WANE television in Indiana.