Three civilians were also killed, Assadullah Khalid said. In addition, nine police officers were wounded in what amounts to some of the heaviest fighting in weeks.
Officials said the fighting erupted after security forces received word that Taliban militants were gathering in and near the village of Sangisar to plan an attack on Kandahar.
Afghan and coalition forces came under attack when they launched a search operation, triggering a battle that lasted almost throughout April 14.
Helicopters from the U.S.-led coalition were called in to support Afghan forces in the battle.
Khalid said no foreign forces were wounded in the battle in Sangisar, a village where the Taliban's fugitive leader Mullah Mohammad Omar once lived.
But the Taliban gave a different account of the fighting. Purported spokesmen for the Islamist militia acknowledged only two or three Taliban deaths and said Afghan and foreign forces had suffered high casualties.
The clash comes amid a surge in violence since the Taliban last month announced they had launched a spring offensive.
This week, coalition and Afghan forces launched a major offensive, dubbed Operation Mountain Lion, against militants in the east of the country.
In other news, the governor of the Baghran district of the southern Helmand Province, Abdul Majeed, was killed in an ambush on April 15, according to the head of the district's police force, Bahaudin Khan.
Despite the rise in violence, the United States plans to pull several thousand troops out of the country this year. Thousands of NATO-led troops are due to deploy in the south where the militants are mostly active.
(compiled from agency reports)