Federal investigators are looking into whether the Chattanooga gunman made several trips to the Middle East, according to US reports.

Muhammad Youssef Abdulazeez, who authorities say killed four US Marines in shootings on two military sites in Tennessee, spent nearly seven months in Jordan in 2014, the Wall Street Journal reported.

A source close to the investigation confirmed to Reuters that authorities are looking at Abdulazeez's travel history to the region, including a possible trip to Yemen.

Counterterrorism investigators are trying to figure out why the 24-year-old Kuwait-born man attacked two military facilities in Chattanooga.

Abdulazeez had not been on the radar of federal authorities until the shootings on Thursday.

Officials said they were investigating whether the attack was inspired by Islamic State or other extremist groups.

The shooting took place at a time when US law enforcement agencies are increasingly concerned about the threat of "lone wolf" terrorist attacks.

Edward Reinhold, special agent in charge of the FBI's Knoxville, Tennessee, division, said a late news conference on Thursday that authorities had not found any evidence linking Abdulazeez to an international terrorist organisation.

The SITE Intelligence Group, which tracks extremist groups, said that Abdulazeez blogged days before the attack that "life is short and bitter".

He added Muslims should not miss an opportunity to "submit to Allah".

Abdulazeez attended high school in a Chattanooga suburb and graduated from the University of Tennessee with an engineering degree.

During his time at the Red Bank High School, he was a popular student, a school friend said.

"He was very outgoing," said Hussnain Javid, a 21-year-old who graduated a few years after Abdulazeez.

"Everyone knew of him."

Authorities say Abdulazeez stopped his silver Mustang convertible outside a naval recruitment office and began spraying the building with bullets.

He then drove across town to the Naval Reserve Center and shot dead four Marines before he was killed.

Three people were also injured, including a US Navy sailor said to have been seriously wounded, and a police officer shot in the ankle.

In response to the attacks, the US Army's top officer on Friday said the military would review security protocols at recruiting centres.

General Ray Odierno told reporters it was too early to say whether the facilities should have armed security guards or other increased protections.

He stopped short of committing to arming military personnel at the recruiting centres, saying it could cause more problems than it might solve.