Provincial council head Ahmad Wali Karzai, who is the brother of Afghanistan's President Hamid Karzai, said one of the terrorists had blown himself up at a gate near a police checkpoint, while another two managed to enter the building.
Karzai, who was not injured in the assault, said police shot at the attackers detonating their explosive vests as a result. Five policemen were killed and at least another three were wounded in the explosion, although the exact number of victims is still unknown.
Taliban militants later claimed responsibility for the attack.
Militants have recently stepped up their efforts to overthrow the government by launching an apparent campaign targeting government offices.
Twelve people were killed and another 16 injured on April 1 when four suicide bombers stormed a provincial council building in Kandahar. A day prior to that attack, a suicide bomber blew himself up near an administrative building in the Dun district, some 15 km (10 miles) south of the city of Kandahar, killing five police officers and three civilians.
Frequent Taliban attacks may pose a serious threat to presidential and municipal elections in the country, scheduled for August 20 as incumbent President Hamid Karzai's term of office ends on May 21.
