NATO reported only light resistance in the villages of Arghandab district, a lush river valley filled with fruit groves that offer militants bountiful defensive positions. The Afghan army says on Monday up to 400 militants poured into the area, just 10 miles northwest of Kandahar city, the Taliban's former power base.
U.S. and NATO officials have repeatedly downplayed the scope of the Taliban push. But the swift military response - 700 Afghan soldiers flew to Kandahar on a moment's notice - and the fighter aircraft dedicated by NATO suggest that keeping Arghandab clear from militants is an urgent priority.
Arghandab is considered a gateway to Kandahar. If militants can gain a foothold there, probing attacks into the city that Taliban leader Mullah Omar once commanded become much easier. Down the line, a large-scale assault could happen.
Elsewhere in Afghanistan, militants killed six NATO soldiers and wounded 10, a sign of the increasing lethality of militant ambushes. Four of the troops killed were British, and two deaths came the east, where the U.S. operates.
The deaths come only days after the Pentagon chief noted that Afghanistan in May saw more American and allied combat deaths than Iraq.
In Kandahar province, the Afghan Defense Ministry said more than 20 Taliban fighters were killed in Tabin and 16 killed in Khohak, two villages in Arghandab. Two Afghan soldiers were also killed, the ministry said in a statement. Twelve other militants were killed in Maiwand, a separate district in Kandahar province.
The governor of Kandahar, Asadullah Khalid, said the Taliban had controlled 10 towns in Arghandab, but government and NATO forces had taken back of four of them.
Khalid said that "a large number" of Afghans have been displaced because of the fighting, and other officials estimated that thousands of Afghans had fled. He said officials have requested help from the U.N.
Helicopters and jets patrolled the skies and smoke rose from fields after exchanges of fire, an Associated Press reporter in Arghandab said. A helicopter landed in a field near the fighting and appeared to evacuate a casualty, he said. Large Canadian military vehicles and Afghan police trucks were moving through the region.
NATO and Afghan forces were moving carefully through Arghandab to minimize civilian casualties and to avoid any bombs planted by insurgents, said Maj. Gen. Carlos Branco, a spokesman for the NATO-led force.
"We are not in a hurry," he said. "The resistance that we face so far has not been significant."
Gen. John Craddock, NATO's Supreme Allied Commander of Europe, wrapping up a visit to Afghanistan, pointed to the Afghan army's response to Arghandab as "an excellent example of its increasing capability," a NATO statement said.
"The fact of the matter is that in less than 24 hours notice the Afghan National Army moved a battalion of soldiers to Kandahar, by using both their own airplanes and ISAF aircraft, from a cold start," Craddock said. "There are not too many nations in the world capable of such a response."
Afghanistan's Ministry of Defense on Tuesday said between 300 and 400 militant fighters were operating in Arghandab. But Canadian military officials who patrolled through Arghandab over the last day reported "no obvious signs" of insurgent activity. But that didn't mean there were no Taliban there, a NATO news release said.
Pentagon officials said reports of hundreds of Taliban in Arghandab were being overstated.
However, Ahmed Wali Karzai, the brother of Afghan President Hamid Karzai and the director of the Kandahar provincial council, said more than 1,500 families had sought refuge in Kandahar, many staying with relatives.
Meanwhile, the British Ministry of Defense said four British soldiers were killed when an explosive was detonated against their vehicle during a patrol Tuesday in neighboring Helmand province. At least one soldier was wounded.
It was one of the deadliest attacks of the year on international troops. Four U.S. Marines were killed in a roadside bomb in nearby Farah province earlier this month, but before that, no more than three international troops had been killed in any one attack in Afghanistan this year.
On Wednesday, two NATO soldiers were killed and 10 were wounded in Paktika province, NATO said. No other details were released, including the soldiers' nationalities. Most soldiers in Paktika are American.
The Taliban assault on the outskirts of Kandahar was the latest display of strength by the militants despite a record number of U.S. and NATO troops in the country. The push into Arghandab on Monday came three days after a coordinated Taliban attack on Kandahar's prison freed 400 insurgent fighters.
Taliban spokesman Qari Yousef told CBS News on Tuesday that many of the militants who had moved into the Arghandab district were freed during the prison break. Yousef often gives exaggerated information - in the same phone call he claimed the Taliban controlled all of Arghandab.
The hardline Taliban regime ousted from power in a 2001 U.S.-led invasion of Afghanistan regarded Kandahar as its main stronghold, and its insurgent supporters are most active in the volatile south of the country.