KANDAHAR, Afghanistan - Afghan and foreign troops will continue to wage the largest offensive since the fall of the Taliban even as the civilian death toll rises, says a key political figure in Afghanistan's volatile south.

But the governor of Helmand province, where coalition forces are battling the insurgents, is urging military commanders to be "much more careful" after more than a dozen civilians were killed in the fighting.

A spokesman for Gov. Gulab Mangal said Tuesday many of the same locals coalition forces are fighting to protect were angered by a spate of civilian deaths in recent days.

"People were upset about civilian casualties," Mateen Zakil said.

"But they were also glad about the operation and they welcomed the operation because they were saying ... if nine or 12 civilians have been killed, other thousands of civilians are going to be freed from the current enemy."

Three Afghan civilians were killed in three separate incidents in Nad Ali district in Helmand province during the offensive, NATO said Tuesday.

Those deaths came after two errant U.S. missiles crashed into a house on the outskirts of the town of Marjah on Sunday and killed 12 people, half of them children.

Afghan officials have said three Taliban fighters were in the house at the time of the attack.

But Zakil told The Canadian Press the governor has warned coalition forces they need to be more careful as the standoff with the insurgents intensifies.

"The governor is urging the coalition forces and also the Afghan forces ... to be much more careful with using the air support, and to be much more careful about civilians, to identify who is the civilian and who is the enemy," Zakil said.

The warning echoes Afghan President Hamid Karzai's earlier call for troops to be "extra cautious while conducting operations to avoid hurting civilians."

Still, the governor has given no thought to calling off the biggest joint operation since the 2001 U.S.-led invasion of Afghanistan, Zakil said, even if civilian deaths soar.

"The operation is not going to be stopped."

Another spokesman for Helmand's governor, Daoud Ahmadi, said Afghan and foreign fighters had so far killed 27 insurgents, captured 11 more and wounded another 20.

Ahmadi blamed the civilian deaths on the Taliban's use of people's homes as shelters.

Having the governor's backing is crucial for coalition forces as they carry out their mission. As the political point man in Helmand province, Mangal holds much sway with the Karzai government as well as local tribal elders.

American, British, Afghan and other coalition troops are storming the insurgent-held town of Marjah and the district of Nad Ali, said to be two of the last major bastions of Taliban control in Helmand province.

The attack is called Operation Moshtarak -- meaning "together" in Dari -- and it is by far the largest offensive staged since U.S. President Barack Obama's decision to send 30,000 more troops into Afghanistan to try to quell a spreading insurgency.

About 15,000 NATO and Afghan troops are part of the offensive.

Three Canadian Chinook helicopters under the escort of four Griffons helped ferry some 1,100 coalition troops into Nad Ali early Saturday morning.

Thirty-four Canadian military trainers are part of the Marjah assault with a kandak, or battalion, of their Afghan army pupils.

The town of Marjah and the district of Nad Ali are some of the world's biggest poppy growing areas, as well as major bomb-making centres and staging areas for suicide bombers.

NATO wants to rush Afghan governance, development aid and security forces into the area as quickly as possible to try to convince locals there's an alternative to Taliban rule.

The insurgent group appeared to suffer a major blow amid reports Tuesday that its No. 2 leader was arrested in a joint CIA-Pakistani sting operation in Pakistan's port city of Karachi.

Mullah Abdul Ghani Baradar is the most senior Afghan Taliban leader arrested since the U.S.-led invasion began in 2001. He is second in influence and power only to the Taliban's spiritual leader, the one-eyed cleric Mullah Mohammad Omar.

It wasn't clear when Baradar was arrested. Some accounts suggest he could have been caught as many as 10 days ago.

The Taliban claim Baradar has not been arrested.

As the Marjah offensive was going on, a separate and unrelated NATO air strike in neighbouring Kandahar province to the east killed five civilians and wounded two. NATO said they were mistakenly believed to have been planting roadside bombs.