It gave no more information immediately about Ciancia, who killed an airport security agent and injured several others yesterday, and who had "strong anti-government views," according to NBC News.
"The suspect in today's LAX shooting has been identified as Paul Anthony Ciancia, 23, a resident of Los Angeles," said an FBI statement yesterday.
The gunman opened fire with an assault rifle in Terminal 3 of the airport, shooting his way through a Transportation Security Administration (TSA) security checkpoint.
An NBC television report suggested Ciancia may have had some link to the Transportation Safety Administration (TSA), and targeted TSA agents as his victims.
Earlier reports said he may have been an off-duty TSA employee, but this was not confirmed.
A new press conference by the FBI, as well as LA law enforcement agencies, was due to be held at 4:00 pm (2300 GMT), the FBI statement said.