Officials said Paul Anthony Ciancia, a 23-year-old Los Angeles man, used an assault rifle to kill a TSA agent and wound several others about 9:20 a.m. PDT.
Los Angeles Airport Police Chief Patrick Gannon told reporters at a news conference the man pulled the gun out of a bag at a security checkpoint and started shooting, and then kept shooting at other locations before police shot him at the airport's Terminal 3 and took him into custody.
"At this point we believe this was a lone shooter," Gannon said.
Police said seven people were treated on the scene for injuries and six were hospitalized.
Los Angeles Police Department anti-terrorism officials were on the scene, but sources told the Los Angeles Times investigators were not aware of any ties to terrorist groups.
Police said Ciancia, who formerly lived in Pennsville, N.J., had written materials in his possession suggesting he held strong anti-government views.
The alleged gunman was not a TSA employee, as initial reports indicated.
Pennsville Police Chief Allen Cummings told NBC News in Philadelphia Ciancia had texted his brother in New Jersey prior to the shooting that he was contemplating suicide.
Leon Saryan, a witness, told MSNBC Ciancia, brandishing his weapon, was walking calmly through a terminal when he asked Saryan if he worked for the TSA.
"All he said was, 'TSA?' Just like that," Saryan said.
The incident occurred in Terminal 3, which was evacuated.
Vernon Cardenas, 45, of West Hollywood, told the Times he was at the airport for a trip to Philadelphia.
"Sitting down, all of a sudden, literally just out of the blue, you hear a rumble in the background and a couple of seconds later, people are running at me," said Cardenas, who is involved in casting for the Fox reality show "MasterChef."
Federal authorities told NBC News the shooter had a rifle or other long gun. A large box of ammunition was at the scene, a law enforcement official said.
The Los Angeles Police Department's bomb squad was trying to clear suspicious packages.
Los Angeles Mayor Eric Garcetti said the situation at the airport had become "static" but he still cautioned people to stay away from the area, as no passengers were being permitted to go into the airport.
The Federal Aviation Administration ordered flights grounded at LAX, the third-busiest U.S. airport and the sixth-busiest in the world, with 1,500 departing and arriving flights daily.
"Due to OTHER / SECURITY and GATE ISSUES and GATE ISSUES, there is a Traffic Management Program in effect for traffic arriving Los Angeles International Airport, Los Angeles, CA [LAX]," a message posted on the FAA website said. "To see if you may be affected, select your departure airport and check 'Delays by Destination.'"
FlightStats, a website that tracks air traffic, said 133 flights had been canceled by mid-afternoon, including 68 departures and 65 arrivals. It said the main road to LAX was closed to all but emergency vehicles, and some inbound flights were being diverted to other airports in the area while other inbound flights were not being allowed to take off from their originating airports.
Delays and cancellations are likely to persist, even after LA reopens, the website said.
LAX was already crowded when the shooting began, due to flight cancellations caused by bad weather affecting major East Coast airports, including Logan International Airport in Boston, LaGuardia Airport in New York and Philadelphia International Airport.
President Barack Obama, following a White House meeting with Iraqi Prime Minister Nouri al-Maliki, said: "Obviously, we've been monitoring, and we're concerned about it. But I'll let the law enforcement folks talk about it directly."
"We will continue stay in touch with our federal and local partners," a White House spokesman said. "The LAPD is leading the response and investigation. We urge citizens to listen to the authorities and follow directions from the first responders on site. The president will continue to receive briefings throughout the day."
Tory Belleci of the cable television show "Mythbusters" tweeted: "Heard gun shots then everyone starting running for the door. Not sure if anyone was hurt. #LAX."