The incident - the latest in a spate of mass shootings in the United States - unfolded at a FedEx operations centre near Indianapolis International Airport in Indiana after 11pm local time on Thursday, police said.

It lasted only a couple of minutes and was already over by the time police responded to the scene, Craig McCartt, the Indianapolis police department's deputy chief, told a news briefing on Friday.

Witnesses described a chaotic attack, as the gunman opened fire in the parking lot before entering the facility and continuing to shoot, leaving victims both inside and outside the building.

Officers found the suspect dead of an apparent self-inflicted gunshot wound.

A FedEx spokeswoman confirmed that the suspect was a former employee at the facility and referred other questions to police.

The suspect has been identified as Brandon Scott Hole, a law enforcement source told Reuters.

NBC News had previously reported that Hole, 19, was the alleged gunman, citing unnamed law enforcement officials.

FBI Indianapolis Special Agent in Charge Paul Keenan said it would be "premature to speculate" on the gunman's motive.

US President Joe Biden, in a statement, said he had ordered flags lowered and reiterated his call for Congress to pass gun restrictions.

"Too many Americans are dying every single day from gun violence," he said.

"It stains our character and pierces the very soul of our nation. We can, and must, do more to act and to save lives."

Friday marked the 14th anniversary of the deadliest school shooting in US history at Virginia Tech, in which 32 people were killed.

"Last night, Indianapolis was revisited by the scourge of gun violence that has killed far too many in our community and our country," Mayor Joe Hogsett said at the briefing.

A FedEx employee, Levi Miller, told NBC he saw a "hooded figure" holding what appeared to be an AR-style semi-automatic rifle who shouted and opened fire outside the facility.

"I thought he saw me, and so I immediately ducked for cover," he said.

Another worker at the air freight facility told local television station WRTV that he was eating when he heard what sounded like "two loud metal clangs" followed by more shots.

"Somebody went behind their car to the trunk and then got another gun," he said.

"Then I saw one body on the floor."

Five people were taken to hospitals with gunshot wounds, including one in critical condition, police said.

Two more were treated at the facility itself by medical staff and released.

Hours after the shooting, employees' family members, friends and colleagues gathered at a "family unification centre" that authorities set up at a nearby hotel.

Some relatives expressed frustration that they were unable to reach workers at the site, where many employees are barred from having their mobile phones by a company policy intended to avoid distractions.

In a message to staff, FedEx Chief Executive Officer Frederick Smith said that the eight victims were all employees.

"First and foremost, I want to express my deepest sympathies to the families, friends and co-workers of those team members," said Smith, who added that the company is co-operating with investigators.

Australian Associated Press