The gunman who shot and killed four Marines Thursday during two attacks at military facilities in Chattanooga, Tenn., has been identified as Muhammad Youssef Abdulazeez, a law enforcement source confirmed to Fox News.

Abdulazeez, 24, was born in Kuwait, a U.S. official told Fox. It was not immediately clear if he was a U.S. or Kuwaiti citizen. He was reported to be from Hixson, Tenn., just across the Tennessee River from Chattanooga.

The law enforcement source said preliminary reports indicate Abdulazeez, who also died, was not on the FBI's radar leading up to Thursday's attacks. A defense official told Fox he was killed by law enforcement officers and did not commit suicide.

The U.S. National Counterterrorism Center said it has seen nothing so far to connect Abdulazeez to any terrorist organization. But it noted that the Islamic State group (ISIS) has been encouraging extremists to carry out attacks in the U.S.

“We are treating this as an act of domestic terrorism,” said Bill Killian, U.S. Attorney for the Eastern District of Tennessee. At a news conference late Thursday, FBI agent Ed Reinhold said there was "no indication at this point that anybody else was involved."

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"Obviously, we're still at the beginning of this investigation," Reinhold said. "We will explore any possibility and that includes whether or not anyone else was involved."

U.S. Attorney Killian added that investigators do not believe that there are any more threats to the general public.

President Obama, speaking from the Oval Office shortly after returning from a trip to Oklahoma, vowed a thorough and prompt investigation.

"It is a heartbreaking circumstance for these individuals who have served our country with great valor to be killed in this fashion," Obama said.

The gunman first shot up a recruiting center before driving seven miles to the Navy Operational Support Center and Marine Corps Reserve Center and killing four Marines before he was shot, authorities said. Sources told Fox News police chased the gunman from the recruiting center to the Center. The entire attack last about half-an-hour.

A well-placed source in Chattanooga told Fox News that one of the Marines who was killed was a "decorated war hero with two Purple Hearts." The youngest was 19 years old, the source said. Defense officials also said late Thursday a female sailor was in surgery after being shot.

Within hours of the bloodshed, law officers with guns drawn swarmed what was believed to be Abdulazeez's house, and two females were led away in handcuffs.

A dozen law enforcement vehicles, including a bomb-squad truck and an open-sided Army green truck carrying armed men, rolled into the Hixson neighborhood, and police closed off streets and turned away people trying to reach their homes.

Details of Abdulazeez's life were just beginning to emerge late Thursday. The Chattanooga Times Free Press reported that he graduated from the University of Tennessee at Chattanooga with a Bachelor of Science degree in electrical engineering in 2012. Before that, he graduated from Red Bank High School with a yearbook photo featuring the quote, “My name causes national security alerts. What does yours do?”

Photos of the yearbook photo were sent to the newspaper, which also reported that he was arrested for driving under the influence last April 20.

The New York Times,citing law enforcement officials, reported Abdulazeez’s father had been investigated several years ago for possible ties to a foreign terrorist organization and at one point was on – but later removed from – a terror watch list.

In a statement, Travis Brickey of the Tennessee Valley Authority, said  the younger Abdulazeez was a student intern "approximately five years ago."

The paper also reported that Abdulazeez's father, Youssuf Abdullazeez, was appointed as a "special policeman" for Chattanooga's Department of Public Works in March 2005. 

Residents and students who knew the suspect said he was a quiet kid, but well-liked.

"He was friendly, funny, kind," Kagan Wagner told the Times. "I never would have thought it would be him."

The shootings began at the all-military recruiting center on Old Lee Highway, where a shot rang out around 10:30 or 10:45 a.m. local time, followed a few seconds later by more gunfire, said Sgt. 1st Class Robert Dodge, leader of Army recruiting at the center.

He and his comrades dropped to the ground and barricaded themselves in a safe place. Dodge estimated there were 30 to 50 shots fired. Doors and glass were damaged at the neighboring Air Force, Navy and Marine offices, he said.

Law enforcement officials told recruiters that the gunman stopped his car in front of the recruiting station, shot at the building and drove off, said Brian Lepley, a spokesman with the U.S. Army Recruiting Command in Fort Knox, Kentucky.

The recruiting center sits in a short strip mall, between a cellphone business and an Italian restaurant, with no apparent special security.

The gunman opened fire next at the Navy Operational Support Center and Marine Corps Reserve Center Chattanooga. The Navy-Marine center, situated in an industrial area of the city, is a fenced-off installation. Its two entrances have unmanned gates and concrete barriers that require approaching cars to slow down to drive around them.

Marilyn Hutcheson, who works at Binswanger Glass just across the street from the center on Amnicola Highway, said she heard a barrage of gunfire around 11 a.m.

"I couldn't even begin to tell you how many," she said. "It was rapid fire, like pow pow pow pow pow, so quickly. The next thing I knew, there were police cars coming from every direction."

She ran inside, and she and other employees and a customer waited it out with the doors locked. The gunfire continued with occasional bursts for what she estimated was 20 minutes. Bomb squads, SWAT teams and other local, state and federal authorities rushed to the scene.

"If it was a grievance or terroristic related, we just don't know," she said.

The Associated Press contributed to this report.