The United Kingdom raised its terrorism threat level to critical, the highest level possible, after the attack Saturday at Scotland's busiest airport.
Two men were immediately arrested at the airport. One was hospitalized with severe burns; early reports that he had died were erroneous.
A third suspect is believed to have died in the Jeep Cherokee that crashed at the airport terminal's main entrance about 3:15 p.m. (10:15 a.m. ET). However, the vehicle was still "in highly unstable condition," and police were waiting to approach it.
William Rae, chief constable of the Strathclyde Police, said part of the Royal Alexandria Hospital in Glasgow was evacuated after a suspicious device was found on the injured suspect. The device was safely taken away and is being examined, Rae said.
Rae said one civilian was treated for a leg injury but there were no other known casualties.
In Glasgow, witnesses described the SUV in flames being driven at full speed toward the building, but Rae -- who is leading the investigation -- said the fire began after the impact.
Witness Jackie Kennedy told the BBC that after the crash, a passenger in the Jeep doused himself with fuel from a can and ignited it, then got out of the vehicle. Airport police used fire extinguishers on him, and he fell to the ground, she said.
"I realized that this was obviously deliberately done -- the fact that the guy was in flames and seemed to be enjoying himself, even smiling," Kennedy told the BBC.
Rae said police want to interview all of the 20 or 30 people believed to have been standing outside the airport entrance when the crash occurred.
The airport was evacuated and all flights diverted or canceled. A number of passengers remained in aircraft on the tarmac, Rae said. It was unknown when the airport would reopen.
John Lennon Airport in Liverpool, England, was shut down later in the day in response to the attack.
Witness Jim Manson said he saw a car "with a couple of guys in it trying to push their way into the airport terminal building."
The vehicle "suddenly caught fire" as one of the two -- himself on fire -- tried to open up the back of the car, Manson told British television.
There was then a small explosion, and the front of the terminal appeared to catch fire.
"Everyone just ran," Manson said. "We're absolutely terrified, you can imagine. The first thing on all our minds was: Is there an accident? Is there a terrorist attack?"
A witness told Sky News that a man fled from the car as it struck the building and was immediately wrestled to the ground by police.
"The Jeep is completely on fire, and it exploded not long after. It exploded at the entrance to the terminal," witness Stephen Clarkson told the BBC.
"It may have been an explosion of petrol in the tank, because it was not a massive explosion."