Afghan government forces have been pursuing Taleban fighters in the south after a major battle.
At least seven policemen were killed in Friday's battle
The clashes in Kandahar province on Friday were some of the most serious in a recent upsurge of fighting.
The governor of Kandahar said seven police were killed and the bodies of 13 Taleban had been found - but that there were reports of up to 41 Taleban dead.
On Saturday further shots were fired as police and army units searched for other insurgents.
Correspondents say it is the first time in a long while that so many Taleban have clashed with police and the national army in the restive province of Kandahar.
Previous violence has consisted of suicide attacks and roadside bombs, says the BBC's Alistair Leithead in Kandahar.
Friday's conflict was sparked after police encountered more than 100 Taleban fighters about 40km (25 miles) from Kandahar city, after they fled an offensive in neighbouring Helmand province, Kandahar governor Assadullah Khalid said.
"Acting on intelligence reports that Taleban have gathered in Sangisar to plan an attack in Kandahar, we launched this operation Friday and the fighting continued from morning to evening," Mr Khalid told a press conference earlier on Saturday.
"In the evening, Afghan army and coalition forces came to support police."
Mr Khalid said nine police and three civilians had also been injured, while 13 Taleban were arrested and survivors were being sought.
"Today we have operations just to find them," he told the BBC.
The village of Sangisar was formerly home to fugitive Taleban leader Mullah Mohammad Omar.
Kandahar's governor has raised concerns about security to cabinet ministers who are visiting the province this weekend.
He is insisting more resources are needed to fight Taleban forces.
Samina Ahmed, South Asia director of the International Crisis Group, said the latest fighting followed a "pattern of activity" repeated over the past couple of years.
"In the spring there's always been a resurgence of Taleban activity," she told the BBC.
"But that said, this is linked this year to the expansion of Nato forces to the south.
"The Taleban... started a few months ago, with targeted attacks, with suicide attacks. And now it appears that they're adding to their arsenal these large-scale attacks."
On Wednesday coalition and Afghan forces launched Operation Mountain Lion, a major military operation against suspected insurgent positions in eastern Kunar province.
Some 2,500 US, British and Afghan troops are taking part in the offensive, which according to the Afghan defence ministry is the biggest joint operation since the Taleban were driven from power in 2001.
Foreign forces gave Afghan troops support in Friday's battle but did not suffer any casualties, reports said.
In other violence, at least three policemen were killed in a roadside bombing near the Pakistani border on Friday.