The fighting took place late on Tuesday near the Helmand province town of Garmser, where Afghan forces have been hunting fighters following last month’s brief takeover of the town by the Taliban.
Local police chief Ghulam Rasool said police had found the bodies of 18 fighters, believed to have been killed in the coalition airstrikes, and four wounded Taliban.
Rasool said an Afghan policeman was also killed during the battle.
Police also confiscated eight AK47s, four rocket-propelled grenades and four motorcycles, he said.
In the country’s capital an explosion destroyed a car belonging to the Afghan finance ministry.
The blast killed the driver and wounded a passenger and a bystander in the southern Beni Sar suburb.
Maj. Luke Knittig, a Nato spokesman, said initial police reports indicated a suicide attacker had detonated his bomb-rigged car prematurely after police tried to stop it.
But Aziz Shams, a finance ministry spokesman, rejected the suicide bombing theory, saying the vehicle was part of a two-car ministry convoy and driven by a “trusted” employee.
Eyewitness Mohammed Amin, 43, said: “A man ran from the car covered in flames screaming ‘help me, help me’ and three police cars were at the scene almost immediately.”
Police found the charred remains of the driver inside the car and took the two wounded people to a medical facility.
Col. Tom Collins, a coalition spokesman, said pamphlets from Taliban leader Mullah Omar had been distributed recently in Afghanistan.
Collins said the pamphlets urged people to rise up against the US and its allies, claiming they were “out to destroy Muslims” and expressing pride in suicide bombers, even if they kill innocent civilians.
Collins said: “We have intelligence reports… there’s no doubt it’s from Omar.”
He wouldn’t elaborate on whether the intelligence indicated that the fugitive militia leader was inside Afghanistan.
Afghan officials have claimed Omar is hiding in Pakistan, which the government there denies.