A law enforcement official told the Los Angeles Times the alleged gunman, 23-year-old Paul Ciancia, originally from Pennsville, N.J., was wounded in the head and shoulder in the shootout Friday.
Gerardo I. Hernandez, 39, a Transportation Security Administration officer, was killed and several other people, including two TSA officers, were wounded.
Investigators were trying to determine the motive. Ciancia allegedly had notes in his backpack describing "disappointment in the government" and indicating he had no interest in hurting "innocent people."
Terminal 3 was still closed Saturday, with no information on when it might reopen, CNN reported.
When the shooting started at about 9:20 EDT Friday, many passengers ran out of the terminal leaving their luggage behind. They would be able to retrieve their abandoned belongings at some time yet to be determined Saturday, LAX officials tweeted.
Three terminals were shut down and evacuated, and flights into the airport were restricted for 6 hours, the Times said.
Several planes filled with passengers were forced to park several hours at a remote area of the airport.
Hernandez was the first employee of the 12-year-old TSA to be killed in the line of duty. The union that represents TSA officers said Hernandez was a behavior detection officer who had recently transferred from Montana, KCBS-TV, Los Angeles, reported.
"No words can explain the horror that we experienced today when a shooter took the life of a member of our family and injured two TSA officers at Los Angeles International Airport," the Times quoted TSA Administrator John S. Pistole as saying in a statement.
Airport police Chief Patrick Gannon said Ciancia removed a rifle from a bag outside a TSA screening area, started shooting and moved into the airport with security officers in pursuit.
The gunman pointed his gun at several people as he made his way through the terminal and asked if they "were TSA," then left them unharmed if they answered no, the Times said.
A witness told the newspaper the gunman cursed the TSA repeatedly. The union representing TSA flight screeners said gunman had never been a TSA officer.
The Southern Poverty Law Center, citing a source it did not identify, said Ciancia was carrying a "manifesto" that contained references to the "New World Order," the Federal Reserve and "fiat currency."
KCBS-TV and KNBC-TV said Ciancia sent a text message before he began his attack to a family member in New Jersey saying he felt suicidal. The TV stations said the family called local police in New Jersey, who called Los Angeles police, who went to Ciancia's apartment in an attempt to check on him.
KCBS-TV said Hernandez was taken to the Harbor UCLA hospital where he died. A second victim taken there suffered a minor shoulder wound and was expected to be released soon, the TV station said.
Three other victims were taken to Ronald Reagan UCLA Medical Center in Westwood. One was in critical condition, one in fair condition and the third was released.
Authorities found a large box of ammunition in the airport.
"There were more than 100 more rounds that could've literally killed everybody in that terminal today," Los Angeles Mayor Eric Garcetti said at a news conference.
A man who said he had been a classmate of Ciancia's at a private high school in Delaware five years ago described him as a loner who had been bullied.
"In four years, I never heard a word out of his mouth," said David Hamilton, who graduated with Ciancia from Salesianum School in Wilmington, Del. "He kept to himself and ate lunch alone a lot. I really don't remember any one person who was close to him."