US authorities have charged a US army veteran accused in a deadly shooting rampage at the Fort Lauderdale International Airport, with offences that could carry the death penalty, while continuing to probe whether "terrorism" was a potential motive.

Federal prosecutors charged Esteban Santiago on Saturday with firearms offences and carrying out an act of violence at an airport, US Attorney Wifredo Ferrer said in a statement.

If convicted, he could face the death penalty or life in prison.

Santiago, 26, was accused of killing five, wounding six and sending thousands scrambling for safety on Friday before authorities shut down the airport in Florida, a major gateway to the Caribbean and Latin America.

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The suspect was scheduled to make an initial court appearance on Monday.

Murder charges could be forthcoming from state prosecutors, but no decision has been made yet, according to the Sun Sentinel newspaper.

Santiago had travelled from Alaska to Fort Lauderdale on Friday.

After retrieving a 9mm semi-automatic handgun and ammunition that he had declared and stowed inside his checked luggage, he allegedly loaded the weapon in a toilet and opened fire in the crowded baggage claim area.

FBI special agent George Piro said law enforcement was continuing to investigate motives for the attack, including "continuing to look at the terrorism angle".

'Mental problems'

A former member of the Puerto Rico and Alaska National Guard, Santiago served in Iraq from April 2010 to February 2011. He ended his service in August.

An aunt, Maria Luisa Ruiz, told the NorthJersey.com news site that Santiago became a father to a baby boy in September, and that he was having mental problems.

"Like a month ago, it was like he lost his mind," Ruiz said. "He said he saw things."

On November 7, Santiago walked into the FBI's Anchorage office and complained that his mind was being controlled by national intelligence agencies, which were forcing him to watch videos of the Islamic State of Iraq and the Levant (ISIL, also known as ISIS).

The "erratic behaviour" led agents to contact local police, who took him to a medical facility for a mental health evaluation, Piro said.

He was not placed on a no-fly list.

Anchorage police chief Christopher Tolley said Santiago came to the FBI office with a loaded magazine, but left his gun and newborn child in his car.

Santiago's weapon was taken by police for safekeeping at the time, and he was able to reclaim it on December 8.

Santiago's brother, Bryan, criticised the way authorities handled his case.

"They had him hospitalised for four days and they let him go. How are you going to let someone leave a psychological centre after four days, when he said he hears voices that the CIA is telling him to join certain groups?" Bryan Santiago told CNN, in a Spanish-language interview the network translated into English.

"Not everyone has the same reaction when they return from war. Some are better, and some, not so much."

The shooting renewed anxieties about airport security, a concern that has loomed large in the post-9/11 era, and shed new light on ongoing US gun-control debates.

The Transportation Security Administration, the agency responsible for security at US airports, allows passengers to travel with unloaded firearms and ammunition as checked baggage.

Senator Chris Murphy, a Democrat from Connecticut, rebuked the government for not taking legislative action to tighten gun laws.

"Political cowardice is the accomplice of every mass shooter," he wrote on Twitter.