Pervez Khattak, a senior leader of Imran Khan's Pakistan Tehrik-e-Insaf party, was quoted by the media as saying: "We have no enmity with the Taliban."
The Taliban are Pakistanis and the incoming government requests the militant group to hold peace talks and work for peace in the region, he said.
The incoming provincial government was ready to hold talks with the Tehrik-e-Taliban Pakistan, Khattak said.
Imran Khan's party is set to form government in Khyber-Pakhtunkhwa with the Jamaat-e-Islami and Qaumi Watan Party.
No group claimed responsibility for the bombings.