The police chief in Helmand province said the attacker detonated his explosives Friday morning as a convoy of foreign troops passed through the town of Gereshk.
The chief says 10 civilians were killed, including two shopkeepers. He doesn't know whether any of the troops were hurt. Most of the NATO soldiers in Helmand are British.
On Thursday, Afghan and NATO troops backed by warplanes drove Taliban militants from villages within striking distance of southern Afghanistan's main city, killing 56 of them, Afghan officials said.
NATO said the 24-hour operation in Arghandab was a swift success that banished any threat to Kandahar and would help reassure Afghans appalled at the embarrassing mass escape of Taliban prisoners from a city jail last week.
Hundreds of families who fled the lush, orchard-strewn valley, which begins just 10 miles from the city, were told they could safely return, the alliance said.
But the declaration of victory was tempered by concern that Afghan officials had unwittingly helped the militants score a propaganda coup by exaggerating the threat they posed.
"No large formation of insurgents were met or spotted. Only minor incidents occurred," alliance spokesman Brig. Gen. Carlos Branco said at a news conference. "The insurgents who were there were evidently not in the numbers or with the foothold that they have claimed."
NATO declined to provide a militant casualty figure and told villagers they could return.
"There is no crisis," Branco said.
Afghan officials had said some 400 insurgents swept into Arghandab on Monday and seized 10 villages and encouraged residents to leave. The area, with good cover against air strikes, is considered a possible launch pad for an attack on Kandahar.
The specter of the Islamic militia retaking the city that served as its capital before U.S.-led forces ousted it in 2001 refocused attention on the militants' resurgence in the intervening six years, despite billions of dollars in aid and the presence of tens of thousands of foreign troops.
The U.S.-led coalition said two of its soldiers died of gunshot wounds and one was wounded in neighboring Helmand province on Thursday evening. It didn't give their nationalities.
On Friday, the province's police chief Mohammad Hussein Andiwal said a suicide bomber detonated his explosives as a convoy of foreign troops passed. Ten civilians were killed, he said, but he did not know if there were any troop casualties. NATO said it had no information about the incident.
NATO officials have sought to play down the threat in Arghandab, but sent 600 British and Canadian troops to support Afghan soldiers, many of whom had been rushed in by air from the capital, Kabul, for the operation.
After 24 hours, Gen. Mohammad Zahir Azimi, spokesman for the Defense Ministry, said the Afghan National Army had taken back the villages. Asked at the news conference with Branco why only 56 militants were killed, he said others may have fled northward under cover of darkness.
He also said the militants planted hundreds of mines "just like in Soviet times" - a reference to the 1980s, when occupying Soviet troops laid large numbers of mines which have since caused thousands of civilian casualties.
NATO and Afghan officials said ground troops were moving methodically through the area on the east bank of the Arghandab River, wary of bombs and keen to avoid civilian casualties.
Mark Laity, another NATO spokesman, said the alliance launched a "limited number" of air strikes overnight. He said no NATO troops were hurt and that the situation on Thursday evening was quiet, but military operations would continue in Arghandab "for a little while yet."
Syed Mohammed, a resident who sent two dozen relatives to Kandahar but stayed behind in the village of Thabien, said gunfights had raged until about 2 a.m.
When he looked out his gate at dawn Thursday, Afghan soldiers shooed him back inside, but not before he saw about a half-dozen bodies - apparently dead militants - in the back of a truck.
"The soldiers were everywhere, even in my pomegranate orchard," Mohammed told The Associated Press by telephone. "They told me to stay home for my own security and because of the mines."
Earlier in the week, he had seen 30 to 40 militants armed with assault rifles and rockets ride through the village on motorbikes, he said.
Azimi said two Afghan soldiers were killed and two more wounded in the operation. Kandahar Gov. Asadullah Khalid said one civilian was killed by gunfire. He also claimed that "hundreds" of militants had been killed or wounded, but didn't elaborate.
An Associated Press reporter on the roof of a shrine overlooking the Arghandab River and the contested area saw Afghan and Canadian troops moving in convoys but no sign of combat, or of any villagers returning.
President Hamid Karzai ordered officials to assist the displaced families, clear any mines and help them return quickly.
Branco said the displaced villagers were staying with friends and relatives in the region and there was "no humanitarian crisis."
Meanwhile, the Taliban announced on a Web site that several suicide bombers had entered Kandahar to attack Canadian and Afghan troops and government officials, according to the SITE Intelligence Group, an organization that monitors militant Web sites.
Branco said police dismantled several bombs in the city Wednesday thanks to tips and Kandahar was "firmly under the control of the Afghan government and its people."
Confidence in that control was badly shaken June 13 when a bold Taliban attack, including two suicide bombings, on the Kandahar prison freed 900 inmates, including 400 Taliban fighters.
Laity said the Taliban were exaggerating, using "words as weapons" to stir panic.
He said the response in Arghandab should allay the fears of Afghans, many of whom doubt Afghan and NATO forces can defeat the insurgency any time soon.
"We know that after recent events like the jailbreak there is concern about our capabilities. This was a fast and very effective response and I think something that all Afghans can take great heart from," he said.