The device exploded near a police van carrying six officers outside the main police station in the town of Bannu, in Khyber Pakhtunkhwa province, district police chief Nisar Ahmed Tanoli told AFP.
Bannu is close to the lawless tribal area along the Afghan border where Taliban and other militants have hideouts.
An earlier blast in the town of Pabbi, just 60 metres (200 feet) from the home of Mian Iftikhar Hussain, the information minister for Khyber Pakhtunkhwa, wounded six people.
In a third blast on Tuesday, a bomb disposal officer was killed on the outskirts of Peshawar while defusing a roadside bomb, officials said.
Pakistan is due to hold a general election sometime in May but concerns about poll security have grown amid a series of attacks, particularly after a series of bombings targeting minority Shiite Muslims killed at least 250 people.
Tanoli said the Bannu device contained two kilograms (four pounds) of explosives and completely destroyed the police van.
"It was a remote-controlled bomb, planted on a motorbike parked outside the police station," he said, adding that the blast killed two civilian passersby.
Police constable Mohammad Shiraz told AFP: "We were six people in the van which was on routine patrol in the city. A sudden blast ripped through the van and all of us were wounded."
Doctor Mahmood Jan at Bannu's hospital confirmed the death toll and said medics had received 14 wounded.
Hussain, a member of the province's ruling Awami National Party (ANP) whose son was killed by Taliban militants, was 25 kilometres (15 miles) away in Peshawar at the time of the blast near his home, police said.
"A bomb exploded near the house of information minister Mian Iftikhar Hussain and wounded three children and three passersby," district police chief Mohammad Hussain told AFP.
The police chief said the bomb was hidden in a pile of gravel being used to build a roadside drain, and television footage showed the blast had left a sizeable crater.
Hussain is well known in Pakistan for speaking out against militants. In July 2010 the Taliban shot dead his only son Mian Rashid Hussain, 28, as he travelled home.
The Tehreek-e-Taliban Pakistan have vowed to kill politicians from the secular ANP. In December a suicide bomber killed Hussain's colleague Bashir Bilour, the number two minister in Khyber Pakhtunkhwa, along with eight other people at a political meeting.
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-The Tehreek-e-Taliban Pakistan have vowed to kill politicians from the secular ANP.-
This is discrimination ... why only ANP leaders ?
This man lost his young son for Pakistan, yet he doesn't get any appreciation from our fundamentalist society.