By Jonathan Allen and Jonathan Kaminsky

Nov 3 (Reuters) - The suspect in a deadly shooting at Los Angeles International Airport wrote that he intended to die after killing at least one security officer, the head of a key congressional security committee said on Sunday, as authorities stepped up patrols at the airport and considered changes to aviation security rules.

Paul Anthony Ciancia, 23, also discussed weaknesses in airport security in the "suicide" note before Friday's attack, Michael McCaul, the Republican chair of the House Committee on Homeland Security, told CNN.

"The other thing he wanted to talk about was how easy it is to bring a gun into an airport and do something just like he did," McCaul said of the note.

An officer with the Transportation Security Administration died in the shooting, the first employee from the agency killed in the line of duty since it was created after the Sept. 11, 2001 attacks. Three others were wounded on Friday.

Extra uniformed and plainclothes police were patrolling Los Angeles' international airport, the world's sixth-busiest, as it resumed full operations on Sunday, said Sergeant Belinda Nettles, spokeswoman for the Los Angeles Airport Police.

Passengers were cautioned to expect delays, Nettles said.

The shooting also has brought calls for improved U.S. airport security. The alleged gunman is believed to have deliberately taken advantage of security vulnerabilities and targeted TSA agents with an assault weapon before police shot and wounded him, ending the rampage.

The federal Transportation Safety Administration is exploring changes to security at Los Angeles' international airport and other airports, TSA Administrator John Pistole told reporters on Saturday.

"We have been discussing what the policies and protocols have been to now," Pistole said. "Obviously, this gives us great concern." He did not additional provide details.

MOTIVE UNCERTAIN

McCaul said the note allegedly written by Ciancia "talks a lot about killing TSA agents, and he said, 'If I just kill one, my mission is accomplished.'"

In a criminal complaint filed on Saturday, investigators said they found a handwritten letter signed by Ciancia in his bag that addressed TSA officials, writing that he wanted to "instill fear in your traitorous minds."

It was not immediately clear whether McCaul was referring to the same note mentioned in the complaint.

Investigators have declined to discuss a possible motive for Ciancia's reported grievance with the TSA.

Authorities charge that Ciancia walked into the airport's Terminal 3 on Friday morning, took out an assault rifle from his bag and opened fire, shooting dead Gerardo Hernandez, a 39-year-old TSA officer at a document checkpoint.