Khairuddin Kaka, the district chief for Zerai, and two of his children were killed in the attack. Three of Kaka's children were injured.
Reports say the bomber detonated his explosives as Kaka and his family stepped out of their house.
In fresh violence in eastern Afghanistan today, NATO said that five civilians were killed and three wounded during a firefight between NATO troops and Taliban militants.
The NATO soldiers were initially hit by a roadside bomb before coming under small-arms and mortar fire.
An alliance statement said the civilian fatalities were "regrettable." It did not say exactly where or when the incident occurred.
(with material from agency reports)