The fighting erupted when militants attacked Afghan police and coalition troops in volatile Ghazni province at about 3 am, an interior ministry spokesman said, labelling the attackers "terrorists".
Two militants and a policeman were killed, the ministry and coalition said.
Three "enemy fighters" were detained and three wounded, a coalition statement said.
"Afghan National Police officers and coalition troops were conducting a combat patrol southeast of Ghazni when they came under fire from an estimated 15 enemy forces on the roof of a building," it said.
The militants had fled after a counter-attack, leaving behind small arms, rocket-propelled grenades and materials to construct improvised explosive devices.
A police official said the militants had launched their attack from a mosque.
Coalition and "enemy" forces also clashed in neighbouring Paktika province early Thursday, leaving one Afghan soldier wounded, the coalition said.
"During the engagement, the coalition provided close-air support. A subsequent coalition patrol reported a number of enemy casualties," it said.
Ghazni and Paktika are among eastern and southern provinces that have experienced regular attacks linked to an insurgency by remnants of the topped Taliban and their Islamic allies, including from the Al Qaeda network.
Insurgency-related violence has killed more than 1,500 people this year, many of them militants.
A US-led coalition of about 20,000 troops, most of them American, is based mostly in the insurgency-hit areas to help Afghan forces hunt down militants.
The United States operation in Afghanistan started in late 2001 when US-led forces invaded to overthrow the Taliban, who had failed to hand over Al Qaeda leader Osama Bin Laden for the September 11 attacks.
US Defense Secretary Donald Rumsfeld travelled on Thursday to southern Kandahar province, the birthplace of the Taliban, to meet troops based there.
He earlier met soldiers at the main base US base at Bagram near the capital Kabul, where he held talks with President Hamid Karzai soon after arriving on Wednesday.
Rumsfeld told troops at Bagram that the US decision this week to cut its force in Afghanistan by up to 3,000 troops had been based on information from leaders on the ground, a coalition statement said.
"The Afghan parliament has been seated, and the number of coalition troops keeps increasing, allowing us to pull out our troops," he said.
Also on Thursday an Afghan court sentenced to death for murder the leader of a gang also convicted of kidnapping and holding an Italian aid worker for three weeks.
Clementina Cantoni, who had been working on a women's aid program in Afghanistan for three years, was snatched from her car at gunpoint in the center of the Afghan capital on May 16 and held for 24 days.
Primary court judge Nooruldin Basit sentenced Timur Shah to 20 years in prison for abducting Cantoni and for the attempted murder of one businessman - and to death for the murder of another.
Shah told the court he had kidnapped Cantoni to win the release from police custody of his mother and other relatives.
"I confess that I kidnapped Cantoni to win the release of my innocent mother and other relatives in police custody, but we did not commit the other crimes," Shah said, his legs in chains.
Police detained Shah's mother after he had kidnapped and killed the businessman. She had known about the abduction but failed to report it to police.
Shah told the court he had received $35,000 and the release of his mother in exchange for Cantoni's release. The state prosecutor, however, cited a confidential document that said the kidnapper had received $200,000 from the Italian Embassy. Afghan officials have denied claims that a ransom was paid for the aid worker's release.
Shah was arrested on September 27 with two members of his gang. One of them was also sentenced on Thursday to 20 years in prison for Cantoni's abduction and to death for the murder. The other was sentenced to 20 years for the kidnapping and attempted murder.
The prosecutor also accused Shah - who was a police criminal investigation director in Kabul under the hardline Taliban regime toppled in 2001 - of two counts of rape, extortion and theft.
Cantoni's kidnapping shocked the substantial aid worker community in the Afghan capital and led many organisations to reinforce security restrictions on their staff.
Last year in November three UN workers were freed after almost four weeks in captivity amid allegations that the government had promised to free 24 Taliban prisoners in exchange for their release.
© 2005 Agence France-Presse
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