Philadelphia Mayor Michael Nutter said late Wednesday night the deceased were five women and a man, but did not release additional information.
One woman was buried under the debris for two hours but escaped with relatively minor injuries, Nutter said.
Search and rescue crews continued to search for victims into the night.
“We do not know how many people were actually in the store at that time and so active search and rescue continues,” the mayor said.
“We’re taking away the debris. We still have an area to be examined, and we are hopeful that we have actually gotten out everyone who was in the building, but at this moment, we do not know for sure.”
Dogs have aided in the effort, which is expected to last at least into Thursday, Fire Commissioner Lloyd Ayers told reporters.
He described the operation as tedious.
Of the 13 people injured and taken to area hospitals, five had been released as of Wednesday afternoon.
The building collapsed onto the Salvation Army Thrift Store next door with an ominous rumble, witnesses said.
“You felt it shake,” Jordan McLaughlin told CNN affiliate KYW. “There was people that actually fell over. People started screaming, they ran across the street. There was people inside the building, you heard them scream.”
He said he helped two people out of the building. Other bystanders, including construction workers, helped four or five others out in the moments after the collapse.
Patrick Glynn said he and others moved rocks and debris to get at people stuck in the rubble.
“I knew that was going to collapse some time soon, and it did today,” he told CNN affiliate WPVI.
“For weeks they’ve been standing on the edge, knocking bricks off, pieces of, you could just see it was ready to go at any time. I knew it was going to happen. I seen it. I said it 10 times. Ask these guys. Every day, I said, ‘It’s gonna collapse, it’s gonna collapse.'”
Another witness, Ari Barker, said he was in his office across the street when he heard “a rumbling, a very unusual sound.” He rushed to the window to see a plume of dust rising from the debris.
Kate Slyman said she felt the ground rumbling as the building collapsed.
“The first thing that came to my mind was a terrorist attack,” she said.
Police described the collapse as an “industrial accident.” The Occupational Safety and Health Administration has been told it was an accident at a demolition site, and it has investigators on the way, spokeswoman Leni Fortson said.
There were no known violations at the site.
“No violations, no complaints that we’re aware of, and all permits were valid,” Nutter said.
The Salvation Army issued a statement saying it had sent a disaster response team to the site and asking that the public pray for its employees, customers and others involved in the collapse.
The collapse occurred in a heavily traveled area of the Philadelphia’s Center City neighborhood. The nearby Mutter Museum is a popular tourist destination that houses medical oddities.
The museum said on Facebook that it would be closed until further notice. While its building was undamaged, the museum said police were using its facilities as a staging area for the rescue operation.