In the insurgency-hit Helmand province, an official was killed in a Taliban ambush on Saturday, police said.
Nine police and several Taliban were wounded in Friday's fighting in Sangisar, a town 40km (25 miles) southwest of Kandahar, said Asadullah Khalid, the provincial governor.
"Acting on intelligence reports that Taliban have gathered in Sangisar to plan an attack in Kandahar, we launched this operation Friday and the fighting continued from morning to evening," he said, according to the Associated Press.
However, a Taliban spokesman, in a telephone call to Al Jazeera's correspondent in Islamabad, rejected Khalid's account.
Mohamed Hanif said 15 Afghan police and one Taliban fighter were killed in Friday's battle.
Khalid said that although major fighting near Kandahar had ended and the area was under control, a search was under way to capture Taliban fighters who had fled to a nearby village.
"We have information that some Taliban managed to escape after suffering a defeat, and our police and soldiers are looking for them," he said.
"We saw the 41 bodies of Taliban at the end of the fighting, but we collected only 11," he said, declining to elaborate on why the other bodies were not retrieved.
The dead in Friday's clash included a district police chief and a district governor was among the wounded, Khalid told Agence France-Presse.
There was no immediate comment on Saturday from the coalition about the fighting in Sangisar, where fugitive Taliban leader Mullah Mohammad Omar lived for several years.
On Friday, a military spokesman in Kandahar, Canadian Major Quentin Innis, said coalition helicopters patrolled during the engagement in Sangisar, but he provided no further details.
An Associated Press reporter in Sangisar on Friday saw helicopters launch missiles but could not see whether the barrage caused casualties.
Kandahar used to be the stronghold of the Taliban until late 2001, when their government was ousted as a result of US-led attacks.
Governor shot dead
Fighting between the Taliban and Afghan forces broke out in Helmand province on Saturday, and seven members of the security forces were killed, Hanif told Al Jazeera.
Police said that Taliban insurgents gunned down a district governor in an ambush on Saturday in Helmand.
Abdul Majeed, the governor for the province's Baghran district, was killed in his car, district police chief Bahaudin Khan told AFP. "Our district governor was martyred today," he said.
Another Taliban spokesman, Yousuf Ahmadi, told AFP by telephone that the movement was responsible for the attack. He said seven police were killed, but this was rejected by Khan.