"One female provincial council member and two soldiers were killed in the attacks."
He said 11 people, including four civilians, had been wounded.
Gul Maki Wakhali, a female member of the Nimroz provincial council, was killed by crossfire, Sadeq Chakhansori, a member of the Afghan parliament who was in Nimroz for a meeting, said.
"It was very heavy fighting. Very bad conditions," The Associated Press news agency quoted him as saying.
"There was one-on-one fighting."
The Taliban has claimed responsibility for the attack, saying it was aimed at government officials.
"Seven bombers and two gunmen are involved in the attack. Two of the bombers have set off their explosives and the others are locked in a gunbattle," Qari Yousuf Ahmadi, a Taliban spokesman, said, before police announced the fighting had ended.
He said his group carried out the attack because provincial officials were trying to persuade Afghans to turn against the Taliban.
The Taliban has launched a series of attacks in the south of the country in recent weeks, ahead of a planned military offensive in nearby Kandahar province.
US forces have gathered on the outskirts of Kandahar city ahead of the Nato operation, which is to be the largest military offensive so far against the Taliban.
The US build-up around Kandahar is a key part of the additional deployment of 30,000 troops ordered by Barack Obama, the US president, in an effort to turn the tide in the Afghan war, now into its ninth year.
By August there will be around 100,000 US troops deployed in Afghanistan, more than three times as many as when Obama took power.