Klurad described one as a "middle-aged" person with minor injuries from being shot in the shoulder. The other had no signs of life when he arrived at the hospital, the surgeon said Friday.
It's presumed that fatality is Gerardo Hernandez, the lone person killed in the shooting according to authorities.
He's the first TSA officer to die in the line of duty since the agency was founded in 2001. The late officer was working as a travel document checker at the time, TSA workers' union and federal sources say.
Gannon said airport police quickly applied first aid to Hernandez, put him in a wheelchair, then rolled him to an ambulance.
"They were absolutely committed to trying to save a life," the police chief said. "Unfortunately, that didn't work out."
Gerardo Hernandez would have turned 40 next week. His widow described him as a "wonderful husband, father, brother, son and friend."
"I am truly devastated," his widow said.
The chaos also affected more than 165,000 passengers on hundreds of flights, as the airport shut down for hours. By early Saturday afternoon, all of it -- including Terminal 3 -- was reopened.
By then, security was out in force -- an "enhanced deployment" that included Los Angeles police department officers and air marshals in addition to airport police, according to Airport police Chief Patrick Gannon. Some were uniformed, others were undercover.
"For today and for the foreseeable future, we'll continue (to have) a very high profile at the curbs and anywhere in those ticketing areas and anywhere on our campuses," the chief said.
Questions about recent repositioning of airport police
The shooting has stirred questions about a recent repositioning of airport police officers around what is known as LAX.
Gannon explained Saturday that, in the past year, he decided to move officers from behind a TSA security checkpoint to in front of it, where they also took on "greater responsibilities" such as monitoring both the arrival and departure floors of the terminal.
"The threat ... at the airport does not exist behind security at that podium, the threat exists from the curbline on," Gannon said. "So ... we have our people stationed throughout the airport.
"That particular individual" -- he added, referring to the nearest police officer to the site of Friday's initial shooting -- "was just moved to the front part of the airport."
At the same time, Gannon acknowledged the trade-off of having the officers roam a larger area, rather than sit at a checkpoint.
"So are they going to be in the exact same (place), exactly where I'd hoped they would be? No," he said. "It didn't happen in this particular case."
Was there anything more behind the shift? A law enforcement source told CNN on Saturday that airport police officers had complained to their union about being "bored with the assignment" of being stationed behind the TSA checkpoint.
Concurrently, TSA management complained that airport police officers weren't paying attention -- sometimes perusing their phones, using iPads or reading books on the job -- according to the same source.
Then came "a fix" agreed to by TSA and airport police management, to keep officers in the public areas but position them in front of the checkpoints, including the one where Friday's shooting began. Part of the deal was that officers would never be more than two minutes from the checkpoint screening area, if needed, according to the law enforcement source.
While Gannon hasn't addressed the claims of "bored" and "distracted" officers, he said Saturday the FBI has indicated his officers "were 60 seconds behind the suspect." However it was decided where they'd be standing, he insisted the two were where they were supposed to be, and did what they were supposed to do.
"Our officers were deployed where they were supposed to be and performed heroically in this particular matter," Gannon said.
TSA Administrator John Pistole called the shooting "a significant event" that will prompt a review of security protocol with partner agencies.
Speaking Saturday from Los Angeles, Pistole said,"This gives us great concern, so we'll look at what our policies are."