Fazal Naeem, a police spokesman, said that a remote-control device was used to target Rehman's car.
"High-intensity explosives were used. The vehicle was completely destroyed," he said.
Rehman, who was a former mayor of Hangu, spent time in jail under the previous military government before benefitting from an amnesty that protected 8,000 politicians, businessmen and officials from corruption charges.
That amnesty was scrapped by the supreme court last month.
Hangu has a history of sectarian clashes between Pakistan's majority Sunni Muslims and minority Shia Muslims.
However, Rehman's son blamed the Pakistani Taliban for the bombing.
"My father was targeted twice before. Taliban and militant groups are involved in this attack," Ateeq-ur Rehman told AFP.
Bagto village is close to Orakzai, home of Hakimullah Mehsud, the head of the country's main Taliban faction.
The blast follows a suicide car bombing at a volleyball game in a northwestern village that killed at least 98 people on Friday.
More than 600 people have died in suspected Taliban attacks since October in an apparent response to a military offensive against Taliban fighters in the south Waziristan region.
About 30,000 troops have secured key towns in the region since the operation was launched on October 17, but thousands of fighters are believed to have fled into the nearby tribal districts of North Waziristan, Kurram and Orakzai.
Meanwhile Pakistani intelligence officials said suspected US drone missiles struck near the town of Mir Ali in North Waziristan on Sunday, killing five men.
Officials said the missiles targeted the house of a well-known tribesman in Mosakki village, about 25km east of Miranshah, the main town in North Waziristan.
The tribesman's grandson was also reportedly killed in the attack which destroyed a vehicle nearby.
"A total of five militants have been killed, two are local and three are foreigners," a Pakistani security official in Miranshah told AFP on condition of anonymity.
Sunday's attack was the third suspected US missile strike in the tribal belt in less than a week.