Two U.S. troops and one Afghan soldier were wounded in the fighting in Miana Shien district of Kandahar province, 150 miles southwest of Kabul, said Khalid Pashtun, spokesman for the provincial government.
U.S. military officials in Kabul could not immediately be reached for comment.
Pashtun said some 300 Afghan troops and a smaller number of Americans launched the operation late Wednesday, skirmishing repeatedly with gunmen in the mountains of an area called Purlaiz.
He said Afghan authorities had recovered the bodies of 13 suspected Taliban killed in the fighting, and arrested eight others who were wounded.
"We seized their Kalashnikovs and the ammunition they were carrying," Pashtun said. "We're still trying to identify them."
The clash appeared to be one of the most deadly since the U.S. military stepped up operations in the spring to combat resurgent Taliban militants.
Earlier this week, U.S. special forces killed several militants in neighboring Zabul province. Four American special forces were killed last Saturday in the same province when a mine exploded under their Humvee.
Also Thursday, the Nobel Peace Prize-winning relief agency Medecins Sans Frontieres suspended operations in Afghanistan a day after five of its aid workers were killed in an ambush claimed by the former Taliban regime.
The assault in northern Afghanistan was the deadliest since the radical Islamic militia was ousted in late 2001.
Two Dutch aid workers, a Norwegian doctor and their Afghan driver and translator were killed when attackers shredded their vehicle with assault rifles and grenades.
"For the time being, our activities will be suspended nationwide," MSF spokeswoman Vicky Hawkins told a news conference. "In the coming weeks we will analyze this event in-depth, but for the moment our priority is to take care of those most affected by this tragedy."
MSF, known in English as Doctors Without Borders, employs 80 expatriates and 1,400 local people in its nationwide operations, and the suspension reflected an immediate increase in fear that an insurgency that has already severely limited operations by relief agencies in the south and east of the country could be spreading.
The organization plans to pull some expatriates back to Kabul and move some other staff to safer locations for the time being.
The implications of the suspension could be grave. MSF is one of the most professional international relief agencies and often sets the trend for others. It has decades of experience in Afghanistan. The organization won the Nobel Peace Prize in 1999.
"We'd adjusted ourselves to a particular level of criminal risk," said Gorm Pedersen, head of Danish aid group DACAAR, one of the main agencies providing wells and water across rural Afghanistan. "That we could handle, but now it may be becoming political. It's most worrying."
President Hamid Karzai expressed sorrow about the attack before leaving Thursday for the United States. But despite daily assaults against soldiers and election workers, Karzai claimed poverty worried ordinary Afghans more.
"I think we are quite all right with security," Karzai said. "We have incidents, sure, we must reduce them. But this is not an alarming thing."
The United Nations took a more alarmed view, saying in a statement it was "deeply shocked and outraged by … yet another tragic and unacceptable act," which confirmed that security had "evolved negatively" in recent months.
The U.N. called for more foreign troops to help Afghans provide security. The world body has raised alarms that the continuing violence could scuttle plans to hold elections this September.
The United Nations and Afghan officials have so far registered some 2.7 million of the estimated 10 million Afghans eligible to vote. But poor security means they have been unable to enter rural areas in much of the south and east.
The U.S. military has insisted the vote can go ahead and announced Saturday that thousands of U.S.-trained troops from the new Afghan National Army will fan out across the country to help 20,000 German-trained police provide security.
In a press conference on Tuesday, President Bush said, "the reports from Afghanistan, at least the ones I get, are very encouraging."
"You know, we've got people who have been there last year and have been back this year report a different attitude. And they report people have got a sparkle in their eye," the president said.
But a General Accounting Office report released Wednesday — while crediting U.S. aid for helping to avert a humanitarian crisis — found that in the last two fiscal years "the postconflict environment in Afghanistan threatened progress toward U.S. policy goals, and poor security, increasing opium cultivation, and inadequate resources impeded U.S. reconstruction efforts."
At least 89 American service personnel have died in and around Afghanistan since the start of the U.S. war on terrorism following the Sept. 11 attacks, including 55 killed in action. But the vast majority of the 360 people killed in violence across Afghanistan this year are Afghan soldiers and civilians.
Taliban rebels and their al Qaeda allies have killed at least 33 aid workers since March last year, most of them Afghans.
The foreigners slain in the latest attack were identified as Egil Tynaes, a 63-year-old doctor from Norway, Willem Kwint, a 40-year-old Dutch man, and Helene de Beir, 30, from the Netherlands.
Police investigating the incident said a farmer saw gunmen ambush the group Wednesday afternoon in a desert area near Khair Khana, a village 340 miles west of Kabul.
"Two men on a motorbike stopped the car and opened fire with Kalashnikovs," Badghis police chief Amir Shah Naibzada said. "He gave a detailed description of the attackers. We're following that up."
Mullah Abdul Hakim Latifi, a purported spokesman for the Taliban, called The Associated Press on Wednesday and said the militia staged the attack. He threatened more attacks and claimed that "international aid workers were working for the policy of America."