Jamaat-ul-Ahrar said it had targeted Christians celebrating Easter, though police have said they are still investigating the claim.
There were scenes of carnage as parents searched for children amid the debris.
Pakistan's president condemned the attack, and the regional government has announced three days of mourning.
At least 300 people were injured, with officials saying they expected the death toll to rise.
All major hospitals in the area were put on an emergency footing after the blast, early on Sunday evening.