Mohammad Youssuf Abdulazeez also spoke out against conflicts in the Middle East, according to the Reuters agency.
Police have said his motives are still being investigated.
Mohammad Youssuf Abdulazeez, who was killed in a shootout with police, suffered from depression, his family said.
In a statement expressing “horror” at the attack, the family said: “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.”
Meanwhile, Reuters and the New York Times say they have seen a text sent the night before to a friend linking to a passage of Islamic text – Hadith 38 – containing the verse: “Whosoever shows enmity to a friend of Mine, I will indeed declare war against him.”
The friend, who requested anonymity, said he thought nothing of the text at the time, but now wonders if it was a hint at the attack to come.
Other friends also told Reuters that Mohammad Youssuf Abdulazeez spoke of his anger about conflicts in the Middle East, including Israeli bombing campaigns in Gaza and the civil war in Syria, after returning from a trip to Jordan last year.
“He had always talked about it, but I’d say his level of understanding and awareness really rose after he came back,” said one of the friends interviewed.
They said he had purchased three guns online following the visit, and used them for target practice.
“It would be premature to speculate on exactly why the shooter did what he did,” FBI agent Ed Reinhold said.
“However, we are conducting a thorough investigation to determine whether this person acted alone or was inspired or directed.”
Mohammad Youssuf Abdulazeez began Thursday’s attack with a shooting spree at a recruitment centre in Chattanooga.
The gunman then drove about six miles to a Navy and Marine reserve centre, where he shot and killed four marines.
A fifth victim, named as Navy Petty Officer 2nd Class Randall Smith, died of his wounds on July 18.
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