The fourth level of the cement deck collapsed to the ground, crushing the floors below it, Stewart said.
"We're still trying to find the safest route to enter the building," he said during an afternoon news conference.
Catherine Woodling, spokeswoman for Atlanta Mayor Shirley Franklin, said the deck has had no code violations since it was built in 2001. It was inspected at that time and cleared for occupancy, she said.
Tevonne Glover said she was working out at a gym across the street when the deck collapsed, trapping her car inside.
"If it had happened five or 10 minutes later, I would have been in there," she said as she stood on the street outside trying to catch sight of her car.
Shaun Dodson, who was eating lunch in his car on the far side of the building, said it sounded like the parking deck was "being demolished."
"I ran around, saw a hole and thought the building was collapsing," he said.
About 10 mangled vehicles were visible from the outside. The parking deck is close to a book store and gym frequented by students from nearby Georgia Tech.
People who had parked in the deck peeked through a chain-link fence trying to get a glimpse of their cars as firefighters inspected the structure. Employees from a nearby lounge handed out water as temperatures climbed to near 90 degrees.
The parking deck is a standalone structure that connects to an office building through a pedestrian walkway, which was not damaged.
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