Local government officials confirmed the incident and said Rahman died after a magnetic IED was detonated against the car he was traveling in.
Another member of the council Abdul Rahim Raza Zada, who was also in the vehicle at the time, was wounded, officials confirmed.
The incident happened close to the provincial council buildings shortly before 1pm local time. This was the second such incident on Tuesday.
The first happened in Kabul city at about 09:45 when Kabul deputy governor Mahbobullah Mohabi was killed in the same type of explosion in PD 9 in Macroyan, Kabul.
His assistant, who had been in the vehicle, was also killed while two others were wounded, the interior ministry confirmed.