Federal authorities say they are investigating the possibility the attacks at a military recruiting center and another military site a few miles away were terrorism. The FBI has taken charge of the case and President Barack Obama promised a thorough and prompt investigation into the attack.
PHOTOS: Gunman targets military sites in Chattanooga
Officials say the lone gunman involved in the attack was also killed and that there was no indication the gunman was on the radar of U.S. law enforcement.
Police say at least one police officer was wounded near a Naval Operation Support Center in Chattanooga.
A U.S. official says the gunman in the shootings has been identified as 24-year-old Mohammod Youssuf Abdulazeez.
He was believed to have been born in Kuwait, and it was unclear whether he was a U.S. or Kuwaiti citizen. The official was speaking on condition of anonymity to discuss the ongoing, sensitive investigation. It was not immediately clear whether the gunman's first name was spelled Muhammad or Mohammad.
He is from Hixson, Tennessee, which is just a few miles across the river from Chattanooga.
Abdulazeez is a graduate of the University of Tennessee at Chattanooga. A University spokesman says Abdulazeez graduated in 2012 with a bachelor's degree in electrical engineering. The Tennessee Valley Authority confirms that he was a student intern at the federally owned utility a few years ago. The U.S. National Counterterrorism Center says it has seen nothing so far to connect Abdulazeez to any terrorist organization.
US Navy Sec. Mabus: "Today, the Navy and Marine Corps team collectively mourn the loss of four heroes" in Chattanooga shooting rampage.— ABC News (@ABC) July 16, 2015
US official: Chattanooga rampage ended when gunman killed in firefight with law enforcement; officer wounded in firefight - @LMartinezABC— ABC News (@ABC) July 16, 2015
This happened at two separate military locations just seven miles apart. An active duty Army recruiter says he was at his office when someone opened fire and he heard 30 to 50 shots.
Sgt. 1st Class Robert Dodge, 36, was working at the Armed Forces Career Center off Lee Highway. There are also offices for Air Force, Navy and Marine Corp there. "We heard one single shot, which kind of sparked our attention. Shortly after that, just a few seconds, the shooter began shooting more rounds. We realized it was an actual shooting, so we then initiated our active shooter drill: getting down low to the ground, moving to a safe location. And we waited until everything seemed to be clear."
Active shooter situation is over. Details forthcoming #chanews— Chattanooga Police (@ChattanoogaPD) July 16, 2015
Witnesses say the shooter pulled up in a convertible silver Mustang and fired from the car and then drove away.
JUST IN: Sources: Chattanooga shooter has been identified; background invest underway involving 100s of US federal staff - @PierreTABC— ABC News (@ABC) July 16, 2015
They say it looked like he had a high-powered rifle and they heard about 20 shots.
The city went into lockdown with people huddled inside restaurants and shops as emergency vehicles rushed up and down the streets looking for the shooter.
Nearby counties were also advised that people stay indoors as a precaution.
Witnesses say they were still shaking long after he sped away and that the whole situation seemed unreal and was terrifying. "We saw the silver convertible Mustang and he was unloading some type of large rifle," one woman said.
"Initially I saw her come into the door and I was telling her to go back and so I pulled off, trying not to because I know he saw me and I didn't want to get hit, so I pulled off and then I tried to go around back where I saw some people escape from the back of the building," another woman said.
ABC7 News contributed to this story.