The Philadelphia Fire Department says eight children are among at least 12 dead.
A fire official said the number of fatalities is "dynamic," indicating the number of those killed could change as the recovery continues.
"Without a doubt one of the most tragic days in our city's history," Mayor Jim Kenney said at a news conference.
First lady Jill Biden tweeted, "My heart is with the families and loved ones of the victims of the tragic fire in Philadelphia."
Gov. Tom Wolf said his "heart goes out to the loved ones left to cope with this heartbreaking loss of life."
Archbishop Nelson Perez reacted to the heartbreaking news by extending "deep condolences to all those in mourning."
Congressman Conor Lamb said he is praying "for the victims of the devastating fire" and their families.
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Rep. Malcolm Kenyatta expressed condolences for the victims.
Bill McSwain said his heart goes out to the families of this horrible tragedy - the whole City mourns with you.
Dr. Mehmet Oz said his heart breaks for the families who lost loved ones.
Attorney General Josh Shapiro thanked first responders and offered his condolences.