MARJAH: U.S. Marines and Afghan soldiers advanced through poppy fields of Marjah on Saturday under withering gunfire from Taliban fighters shooting from mudbrick homes and compounds where families huddled in terror.

President Hamid Karzai urged NATO to do more to protect civilians during combat operations to secure Marjah, a southern Taliban stronghold and scene of the biggest allied ground assault of the eight-year war.

NATO forces have repeatedly said they want to prevent civilian casualties but acknowledged that it is not always possible. On Saturday, the alliance said its troops killed another civilian in the Marjah area, bringing the civilian death toll from the operation to at least 16.

Addressing the opening session of the Afghan parliament in Kabul, Karzai held up a picture of an 8-year-old girl who lost 12 relatives in a NATO rocket attack during the second day of the Marjah assault, which began Feb. 13.

Karzai said NATO had made progress in reducing civilian casualties and thanked the top commander, Gen. Stanley McChrystal, for "standing with us honestly in this effort." But Karzai said more needed to be done to protect civilians caught up in the fighting.

"We need to reach the point where there are no civilian casualties," Karzai said. "Our effort and our criticism will continue until we reach that goal."

The Marjah operation is a major test of a new NATO strategy that stresses protecting civilians over routing insurgents as quickly as possible. It's also the first major ground operation since President Barack Obama ordered 30,000 reinforcements to Afghanistan to curb the rise of the Taliban.

Once the town is secure, NATO plans to rush in a civilian Afghan administration, restore public services and pour in aid to try to win the loyalty of the population and prevent the Taliban from returning.

As the assault entered its second week, Marines and Afghan soldiers faced hours of sporadic but intense gunfights from insurgent snipers — often firing from compounds where families could be seen taking shelter. Troops crouched for cover in muddy ditches, firing rifles, machine guns, and grenades as Taliban bullets whizzed by.

"We've been hurling lead all day," said Lt. Carl Quist, who commands a platoon in the 3rd Battalion, 6th Marine Regiment.

U.S.-led troops have been pushing south from the town center against a pocket of Taliban fighters.

"They are running out of space now, that's why they gotta fight and stand their ground," Sgt. Melvin Adair, 28, of Clinton, Maryland, said of the Taliban.

A NATO statement said fighting was raging in the northeast and west of the town "but insurgent activity is not limited to those areas."

A Marine spokesman, Capt. Abe Sipe, said Taliban fighters seemed to be running low on supplies and ammunition "but at the same time we do expect them to be putting up resistance for some time."

Twelve NATO troops have died so far in the offensive in Helmand province, and senior Marine officers say intelligence reports suggest more than 120 insurgents have died.

NATO reported two more service member deaths — one Friday by rocket or mortar fire in eastern Afghanistan and another Saturday in a bombing in southern Afghanistan. Neither was related to the Marjah area fighting, NATO said without identifying the victims by nationality.

By sundown Saturday, Marines reached a large abandoned school compound that residents warned had been entirely rigged with explosives. A small line in the dirt could be seen runnng through the unpaved street. Residents said the line was a marker for the minefield around the compound.

"Nobody, no motorbike nor car, has gone on this road for five days," said Mamad Jan, a terrified farmer who huddled in one room of his home with his ailing wife and children. All other residents had fled the area ahead of the expected showdown.

"I can't leave. My wife just gave birth," Jan told the Marines, some of whom handed out their food rations to his hungry family before taking cover from sniper fire.

The offensive had been moving slowly due to stubborn Taliban resistance and strict NATO rules aimed at limiting casualties among the estimated 80,000 inhabitants of the town.

Troops cannot call in airstrikes to clear snipers from buildings if they believe civilians are inside. Troops cannot fire on suspected insurgents unless they are seen carrying a weapon or discarding one.

The U.S. general who oversees operations in Afghanistan and the Middle East defended the policy of restraint, saying it was scoring points with the Afghan population whose support is essential to turning back the Taliban. The United Nations says most of the civilian deaths last year were due to Taliban attacks.

"We're going to be able to beat the enemy around the head with civilian casualties that he is causing," Gen. David Petraeus said at Princeton University.

Most of the civilian deaths came on the second day of the operation when a pair of rockets struck a building on the outskirts of town, killing 12 people — at least nine of them civilians including the family of the 8-year-old girl. The alliance first said the rockets strayed 300 yards (meters) off course but later acknowledged they hit the intended target.

The civilian was killed Friday after he dropped a box which soldiers feared contained a bomb and began running toward a coalition position, NATO said. The box contained materials that could be used to make a bomb but no explosives NATO said.

"This is truly a regrettable incident, and we offer our condolences to the family," said a NATO spokeswoman, Navy Capt. Jane Campbell, said in a statement.

In a cemetery marked by green and white flags in Helmand's provincial capital of Lashkar Gah, 20 miles (30 kilometers) northeast of Marjah, men buried one Marjah resident who died of his injuries suffered in what his brother said was coalition bombing three days ago.

"I buried him here, because I couldn't take him back to my village," the brother, Sayed Wali, a thin man in a faded blue tunic, told Associated Press Television.