Nearly 5,000 coalition forces, including about 600 Canadians, were involved in the operation west of Kandahar, along with soldiers from the Afghan National Army and Afghan police.
In two separate battles late Saturday afternoon, the coalition troops suffered no casualties, but killed at least 35 Taliban fighters, wounded more than 20 others and captured more than a dozen insurgents, according to Helmand's provincial police chief.
The battles happened in Sangin, where most of Canada's combat troops stationed in southern Afghanistan had been fighting since early Saturday.
A Canadian reconnaissance platoon and another infantry squad were reportedly ambushed, although none of the soldiers were hurt as they fired back during short, fierce battles.
Canadian coalition officials were unable to confirm the number of dead or whether Canadians were involved in the attacks that also led to the arrests of 14 Taliban.
In the battles for control of Sangin, eight Taliban fighters were killed and four others captured in one late afternoon altercation, the police chief said.
Then, about an hour later, 27 Taliban were killed, 18 wounded and another 10 arrested.
Canadian officials had earlier reported that 10 Taliban were killed during the coalition's first offensive push into Sangin involving Canadian and American ground troops and British paratroopers.
Coalition troops hope to create a "security pocket" in Sangin, where meetings can be held among local elders and military and Afghan government officials to talk about reconstruction efforts.
"This operation, when it wraps up, will be followed by a Shura," said Canadian coalition spokesman Maj. Scott Lundy.
"That's one of the meetings which will occur in which they can discuss the reconstruction that they require, and look toward the future as opposed to what they now face, which is coercion, bullying at the hands of the Taliban."
The coalition offensive is considered the final push of an operation known as Mountain Thrust, which has been underway since mid-June, aimed at cutting off the Taliban's financial centre.
However, there has been speculation that much of the Taliban resistance has already moved into Oruzgan province, north of Kandahar.
That's where Canada is expected to help Dutch soldiers establish a significant presence for NATO's International Security Assistance Force, or ISAF.
Expatriate Canadian sources say they expect the violence in Oruzgan to only get worse in the months ahead.
In Zabul province east of Kandahar, an American soldier was killed Sunday in a separate firefight involving coalition forces in the Day Chopin district.
ISAF is slated to take over command of international military operations in and around Kandahar by the end of this month.
