CHATTANOOGA, United States (AFP) - Investigators are searching for evidence that the man who killed four US marines may have contacted Islamic extremists either online or during overseas travel but so far have found nothing, the FBI said Friday.

Mohammad Youssuf Abdulazeez, 24, opened fire on two military centres in Chattanooga on Thursday, gunning down the four Marines and wounding three people before dying in a shootout with police.

Authorities have said they are treating the case - a grisly scene reminiscent of other shooting rampages at US military installations - as an "act of terrorism."

But, after a senior US lawmaker said he believed the evidence pointed to an attack inspired by the Islamic State in Iraq and Syria (ISIS) extremist group, the FBI warned against jumping to conclusions about a possible motive.

"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 of Abdulazeez, a naturalised US citizen who was born in Kuwait.

The FBI has asked foreign intelligence agencies to help trace his movements and activities abroad, and analysts will be tracing his activity on social media, Reinhold said.

"We obviously want to know what his thoughts were and who else he was associating with," he told reporters.

In an apparent blog post written Monday, Abdulazeez said Muslims should not let "the opportunity to submit to Allah... pass you by," according to the Site Intelligence Group, which monitors extremist activity on social media.

Michael McCaul, chairman of the US House Homeland Security Committee, said earlier Friday that he believed the attack was inspired by the Islamic State group.

"My judgment, in my experience, is that this was an ISIS-inspired attack," McCaul told a press conference in Florida.

"This will no doubt be proclaimed as a victory for them. But we will have the final word in this war against them."

FOREIGN TRAVEL IN SPOTLIGHT

Investigators were especially looking at Abdulazeez's foreign travel, with a reported trip to Jordan last year of particular interest.

Bassam Issa, president of the Islamic Society of Greater Chattanooga, told CNN that Abdulazeez had moved overseas to live with relatives about two years ago.

"My understanding is recently he had come back... and was working with a company in Nashville," Issa told CNN.

The Kuwaiti interior ministry issued a statement Friday confirming that Abdulazeez was born in Kuwait and had last visited in 2010 for three weeks, but was of Jordanian descent.

The gunman had not given authorities any reason to place him under surveillance prior to Thursday's attacks, Chattanooga mayor Andy Berke said.

"We certainly didn't have any indication that he was a threat or that yesterday something was going to happen," Berke said.

LONE WOLF?

Although no motive has been formally established so far, the incident fuelled fears of so-called "lone wolf" actors - attackers with no known affiliation to an extremist group who are extremely difficult to detect.

"What keeps me up at night is the one case we don't know about," McCaul said. "This is the event we've been most worried about, and then it happened."

US media reports described Abdulazeez as having had a traditional American upbringing, including participation on school sports teams.

He graduated from the University of Tennessee at Chattanooga with a degree in engineering in 2012.

Scott Schrader, who coached Abdulazeez in mixed martial arts, told CNN he "seemed like the all-American kid."

There was evidence, however, that he came from a troubled family.

Divorce papers filed by his mother and obtained by AFP allege that his father beat his wife and five children.

His father was also reportedly investigated for ties to a terrorist group, but ultimately cleared.

Abdulazeez had a brush with the law in April when he was arrested for driving under the influence, local media reported.

'IT HIT REALLY HARD'

The victims were identified as: Gunnery Sergeant Thomas Sullivan; Staff Sergeant David Wyatt; Sergeant Carson Holmquist; and Lance Corporal Squire Wells.

Wells joined the Marines last year. The other three men had each served at least two tours of duty in Iraq or Afghanistan.

Shaken residents gathered at memorials Friday to mourn them.

"It hit really hard," Ansley Chilton, a student at the University of Tennessee-Chattanooga, told AFP.

"I wanted to come to honor the victims, especially since it was so close to home."

Chattanooga police chief Fred Fletcher heaped praise on the officers who helped prevent further loss of life.

He described how the officer who was shot in the ankle was dragged to safety by his colleagues "and bravely returned fire to ensure that he was safe and the gunman remained engaged."

"They are my heroes. I have never been prouder to be a police officer than I was yesterday and today," he said.