The attack on the outskirts of Peshawar killed the leader of an anti-Taliban militia, Israr Khan, and two aides as he passed through a market in the village of Matni, said police official Khurshid Khan. Three more people were injured.
The government supplies a string of militias with arms and money to fight the Taliban militants.
The deadliest blast was a suicide attack at a mosque inside a religious school in South Waziristan that killed 26 people and injured 40 more, said an intelligence official in the region. He spoke on condition of anonymity in line with the orders set down by his agency.
He said Maulana Noor Mohammad, a former lawmaker who ran the school, was among the dead.
Yar Mohammad, a local tribesman who was present inside the mosque, also said it was a suicide blast.
There was no claim of responsibility, though Islamist militants have often attacked clerics or others who do not support them. It was unclear whether Mohammad fell into that category. Militant and tribal factions also fight among themselves.
Earlier, a bomb exploded inside a school during a meeting of elders in Kurram tribal region, killing seven people.
Local official Khalid Umerzai said the elders at the meeting were discussing a disagreement over ownership of the school building. It wasn't clear if the blast was tied to that dispute or if it had been launched by Islamist militants.
The army has launched offensives in South Waziristan and Kurram over the last 18 months.
There is little or no government presence in either area.
South Waziristan was affected by the floods that have swept Pakistan over the past month, with 18 bridges washed away and about three dozen deaths in the tribal area.
Associated Press Writer Riaz Khan in Peshawar and Ishtiaq Mehsud in Dera Ismail Khan contributed to this report.