CHATTANOOGA, Tennessee -- The family of the gunman who killed four Marines and a sailor in Chattanooga says he had suffered from depression for many years and "was not the son we knew and loved."
"It grieves us beyond belief to know that his pain found its expression in this heinous act of violence," the family of Muhammad Youssef Abdulazeez said in a statement issued Saturday through a lawyer.
Law enforcement officials did not return calls seeking comment on the family's assertion that Abdulazeez was suffering from depression.
Counterterrorism investigators, meanwhile, continued to interview Abdulazeez's acquaintances and delve into his months-long visit to Jordan last year, looking for clues to who or what might have influenced him and set off the bloodshed Thursday.
Officials caution it's too early to say if he was inspired by the Islamic State of Iraq and Syria (ISIS) or other terror groups, reports CBS News correspondent Jericka Duncan. But among the things that are being looked at was Abdulazeez losing his job at an Ohio power plant after 10 days in 2013. Last April, he was pulled over for DUI.
Friends also say Abdulazeez told them he was at a firing range recently.
"One of the scary and dangerous dimensions of this case is the fact that perhaps we couldn't have done more to prevent the attack," said Juan Zarate, CBS News national security analyst. "And I think that's really the danger of these kinds of potential lone wolf cases."
The 24-year-old Kuwait-born Abdulazeez opened fire at a military recruiting office and a Navy-Marine operations center a few miles apart.
Family members said they are cooperating with the investigation.
"We understand there are many legitimate questions that need to be answered," they said. "Having said this, now is the time to reflect on the victims and their families, and we feel it would be inappropriate to say anything more other than that we are truly sorry for their loss."
A law enforcement official who was not authorized to discuss the investigation and spoke on condition of anonymity said FBI agents were continuing to interview people Sunday and reaching out to a broader circle of potential contacts and acquaintances.
The official said that investigators were especially interested in Abdulazeez's trip to Jordan and were trying to determine whom he met with, what he did and whether he might have gone or tried to go anywhere else.
The president of the Islamic Society of Greater Chattanooga said Abdulazeez's father told him he felt blindsided by the attack.
"He told me that he had never seen it coming, and did not see any signs from his son that he would be that way and do something like that," Bassam Issa said.
Meanwhile, governors in at least a half-dozen states ordered National Guardsmen to be armed, and Florida Gov. Rick Scott moved his state's Guard recruiters from storefronts in urban areas to armories.
In Tennessee, where the shooting occurred, Gov. Bill Haslam has called for a review of security policies and procedures at National Guard armories and other military installations in the state.
"We don't want to leave our folks out there as targets when we've had such a horrible event happen just three days ago," Haslam told NBC television's "Meet the Press" on Sunday.