At least six Afghan policemen or soldiers were among the dead in the attack in Lashkar Gah, the capital of Helmand province, when a bomber detonated explosives strapped to his body at the front of the governor's compound, officials said.
Many of the civilians killed were reportedly queuing to complete paperwork so that they could go on the Hajj pilgrimage to Makka.
General Mohammad Nabi Mullahkhail, the provincial police chief, said another 18 people were wounded in the attack.
A provincial government spokesman said that Afghan soldiers had spotted the bomber who was trying to get into the governor's compound. They tried to arrest him when he blew himself up near a police post.
Italian troops from the International Security Assistance Force (ISAF) confirmed that there had been an explosion near the compound and said it might have been directed at forces guarding the premises.
Muhammad Hanif, a spokesman for the Taliban, later told Aljazeera that the group said it carried out the attack and that on an Italian convoy.
In the second incident, a bomb struck the convoy of Italian troops on patrol on the outskirts of the Afghan capital, killing one soldier and wounding five others, the force said.
An Afghan child travelling in a vehicle behind the convoy was also reportedly killed in the blast.
Italy has almost 2,000 troops in Afghanistan as part of the ISAF force.
Meanwhile, a third attack in the south-eastern province of Khost was averted when a bomber attempting to attack a convoy of US-led troops blew himself up prematurely, although local police officials said the man was shot dead by troops.
A US military base in Khost province was also hit by rockets, an Aljazeera correspondent in Afghanistan reported, quoting local Afghan security officials.