The 26-year-old suspect, identified as Esteban Santiago who had been treated for mental health issues, drew a gun from his checked luggage on arrival at the busy airport and opened fire in the baggage claim area Friday, authorities said.
Santiago, who was wearing a Star Wars t-shirt, was taken into custody. His motive was not immediately known.
The shooting took place yesterday in Terminal 2 in the baggage claim area, outside the TSA checkpoint, police said. Air Canada and Delta Airlines operate out of Terminal 2.
People were corralled onto the tarmac and paramedics were at the scene, police said. All services at the airport have been temporarily suspended, the airport tweeted.
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A Iraq war veteran, Santiago was discharged from the Alaska Army National Guard last year due to unsatisfactory performance.
In November, Santiago paid a visit to the FBI office in Anchorage, telling agents he was being directed by a US intelligence agency to fight for ISIS, CNN reported, citing law enforcement sources.
The military said Santiago's nine years of service in the guard included one 10-month tour of Iraq, where he was awarded a combat action badge.
"The President (Barack Obama), on behalf of the American people, extended his sincere condolences to the families and other loved ones of those killed and noted that his thoughts and prayers are with the wounded," said Ned Price, Spokesman of National Security Council, the White House.
Federal authorities will continue to assist the ongoing investigation into this horrific shooting, Price said.
"Monitoring the terrible situation in Florida. Just spoke to Governor Scott. Thoughts and prayers for all. Stay safe!," US President-elect Donald Trump said in a tweet.
Hundreds of people were standing on the tarmac as dozens of police cars and ambulances rushed to the scene.
Police received a call just before 1300 local time (2330 IST yesterday) about shots fired at Terminal Drive.