The 71 insurgents were killed when they attacked police in Panjwayi district in southern Kandahar province late Saturday, said Niaz Mohammad Sarhadi, the district chief.
NATO troops used artillery and aircraft in the clash that lasted until early Sunday, said Maj. Toby Jackman, a spokesman for the force.
Four police and one Afghan soldier were killed, officials said. Three police and five soldiers were wounded. The bodies of the some of dead militants were found scattered through orchards alongside their weapons, Sarhadi said.
During a clash Saturday against Taliban militants in eastern Kunar province, three U.S. soldiers were killed and three others wounded, said U.S. military spokesman Col. Tom Collins.
American troops in that area are hunting for Taliban fighters and extremists close to Osama bin Laden's al Qaeda network in remote mountains hugging the Pakistani border.
In southern Uruzgan province, an American and an Afghan soldier was killed and three other Americans wounded in a four-hour clash with more than 100 insurgents, according to a NATO statement.
The troops used artillery and air support to repel the insurgent attack, a NATO statement said.
U.S. and NATO forces are facing a re-energized and increasingly powerful Taliban, reports CBS News correspondent Joie Chen.
"There are people today, particularly Afghan journalists and Pakistani journalists who monitor this very closely, who say Afghanistan is a lost cause," said CBS News consultant Jere Van Dyke.
As the violence escalates, so too has the American troop presence. Chen reports there are now 22,000 U.S. military personnel in Afghanistan – the highest number since the 2001 invasion.
But, all of it has happened in the shadows of the world stage.
"People feel that the war in Afghanistan is a forgotten war," Van Dyke said. "What people really have to know is that more U.S. soldiers die in Afghanistan per capita than die in Iraq."
Collins said the troops in Uruzgan are part of a U.S. team training the fledgling Afghan National Army. Currently about 22,000 U.S. forces are in Afghanistan along with 20,000 NATO-led troops.
The slain American was identified by family members as senior airman Adam Servais, 23, of Onalaska, Wis. The four-year veteran was with Air Force Special Operations.
Officials said they didn't have details on insurgent casualties.
The fighting was reported to be some of the heaviest in recent months and came as war-battered Afghanistan celebrated its independence day.
Thousands gathered Saturday to mark Afghanistan's independence from British rule in 1919, following the third Anglo-Afghan war. Repeated wars and conflicts have devastated the country of 25 million people in the last three decades, with scars still visible on buildings and large swaths of minefields.
Meanwhile, a mine in the country's restive south killed a local police commander and an ambush by suspected insurgents left a spiritual leader wounded.
The officer was killed when his vehicle hit a freshly planted mine in Sori district of southern Zabul province on Friday, said Noor Mohammad Paktin, the provincial police chief.
Separately, suspected Taliban militants wounded Mrich Agha, a spiritual leader in the southern Kandahar province on Saturday, said Dawood Ahmadi, the governor's spokesman. Agha's driver was killed in the ambush, Ahmadi said.