At least seven children are among the dead, an official from the Philadelphia Fire Department told reporters.
The blaze began at around 06:00 local time (11:00 GMT) in a public housing block in the north of the city.
Deputy Fire Commissioner Craig Murphy told reporters it was one of the worst fires he had ever seen.
"We plan on making sure that this tremendous loss of life did not happen in vain," he said on Wednesday.
He added that eight other residents had managed to escape the building.