The first incident occurred Sunday morning at an election office at the Orakzai Agency and Kohat border, Geo News reported.
The bomb, containing 22 pounds of explosives, detonated at the joint office of independent candidate Syed Noor Akbar from Orakzai Agency, and Awami National Party candidate Khurshid Begum, from Kohat, police said.
Neither candidate was injured. At least five people died and 21 others were injured in the blast.
The second blast was in Peshawar where at least three people died and eight were injured, Geo News reported.
The explosion was at the office of an independent candidate for Bara Khyber Agency, Nasir Khan. Khan was uninjured.
In response to the bombings, President of the Pakistan Muslim League-Nawaz Mian Nawaz Sharif called on politicians to unite against terrorism.
"We just cannot let a handful of militants deny us elections. We will have to stand as one man against their anti-Pakistan designs. Elections shall be held as scheduled no matter what," he said in a statement.