Investigators believe Abdulazeez may have family in Jordan, making a visit to that country highly likely, one of the sources close to the probe said. He may have made several stops, and a visit to Yemen has not been ruled out.
A trip to Yemen, long viewed as a training ground for Islamic militants, would raise special concern. Two brothers of Algerian extraction who led an attack on the Paris office of the satirical magazine Charlie Hebdo in January had visited Yemen in 2011.
U.S. investigators are probing the suspect's travel history as part of efforts to determine whether he had any contact with militants or militant groups, but they have no firm evidence so far that he did, one source close to the probe told Reuters.
Beyond direct contacts, law enforcement officials have said they are investigating whether Abdulazeez was inspired by Islamic State or similar militant groups. Islamic State had threatened to step up violence in the holy fasting month of Ramadan, which ends on Friday evening.
Islamic State claimed responsibility after a gunman killed 37 tourists in Tunisia in June, the same day as an attack in France and a suicide bombing in Kuwait.
Abdulazeez, who grew up in a Chattanooga suburb and studied engineering at a local university, is believed to have traveled to the Middle East, where his family has roots, between April and November 2014, according to one of the sources, who was not authorized to speak on the record.
The suspect, who was seen on Thursday driving an open-top Ford Mustang, sprayed gunfire at a joint military recruiting center in a strip mall, riddling the glass facade with bullet holes, then drove to a Naval Reserve Center about 6 miles (10 km) away, where he killed the Marines before he himself was killed.
Among the injured in the shooting, which comes at a time when U.S. military and law enforcement authorities are increasingly concerned about the threat 'lone wolves' pose to domestic targets, was a sailor who was critically wounded.
The SITE Intelligence Group, which tracks extremist groups, said Abdulazeez blogged on Monday "life is short and bitter" and that Muslims should not miss an opportunity to "submit to Allah." Reuters could not independently verify the postings.
While there is no specific evidence about what might have prompted the suspect to carry out the shooting, they believe family or psychological issues may have contributed, according to the second source, who was not authorized to speak on the record.
His father, Youssuf Abdulazeez, who attended Texas A&M University and comes from Nablus, on the West Bank, according to his Facebook page, appears to be a high achiever. He worked since at least 2005 as a soil engineering specialist for Chattanooga city's public work's department, according to public records. A 2005 city resolution authorized the father as an unarmed policeman as part of his work.
The suspect appears to have been following in his father's footsteps, at least in terms of his occupational pursuits. According to a resume believed to have been posted online by Abdulazeez, he attended high school in a Chattanooga suburb and graduated from the University of Tennessee in 2012 with an engineering degree. His work experience includes an internship with the Tennessee Valley Authority, a regional power utility.
Years ago, the father came under investigation by a Joint Terrorism Task Force for possible connections to a militant group, the second source said, but he was cleared of any association with terrorism or wrongdoing. It is possible but not certain that the probe resulted in the father's name being placed on a terrorist watch list, according to that source.
Abdulazeez, who was raised as a Muslim, was scheduled to appear in court on a charge of driving under the influence in July, according to media reports.
He was arrested in April after his car was seen weaving between lanes. The arrest report said Abdulazeez smelled of alcohol and marijuana and was unsteady on his feet.
Four Marines who were killed were identified as Gunnery Sergeant Thomas Sullivan, 40, of Springfield, Massachusetts, who earned a Purple Heart; Skip Wells, 21, of Marietta, Georgia; David Wyatt, of Chattanooga, and Sgt. Carson Holmquist, 27, of Jacksonville, North Carolina, according to media reports. The U.S. Defense Department has not yet released any of the names.
The Islamic Society of Greater Chattanooga, where the New York Times said the suspect and his family worshipped, canceled all activities to celebrate Eid, marking the end of Ramadan, the Islamic holy month of fasting, according to its website.
“We condemn this act in the strongest possible terms as one of cowardice and hate," Bassam Issa, the society's president, said in a statement.
A community gathering will take place at 5:30 p.m. (6.30 p.m. EDT) on Friday at Olivet Baptist Church in Chattanooga. The Islamic Society said on its website that it was "vital, crucial and essential" that all Muslims in the area attend the event.