NATO's new secretary-general pledged Wednesday that the alliance would remain in Afghanistan despite flagging support in many nations from voters anxious over rising deaths among civilians and Western forces.

Anders Fogh Rasmussen flew to Kabul to meet with politicians and military leaders two days after taking control of an alliance that is struggling to maintain its cohesion and relevance as it battles Taliban insurgents thousands of miles from Europe.

"I can assure you and the Afghan people that we will stay and support you for as long as it takes to finish our job," the former Danish prime minister told Afghan President Hamid Karzai at a joint press conference in the capital, Kabul.

Some 65,000 troops from 42 nations serve in a NATO-led force hobbled by disagreements over the need for more troops, and widely divergent national restrictions on when troops can fight. Recent polls show majorities in Britain, Germany and Canada oppose sending more troops to Afghanistan, even as President Barack Obama moves in U.S. forces.

July was the bloodiest month for the U.S. and NATO in the nearly eight-year war, and the U.N. says civilian deaths soared by 24 percent in the first half of 2009.

Civilian deaths in Western airstrikes and ground operations aimed at Taliban forces are causing deep resentment among Afghans.

Outraged villagers near the southern city of Kandahar said a Western airstrike before dawn Wednesday had killed three children and a man in their village of Kowuk.

Fogh Rasmussen did not address the charges but said, without providing figures, that there had been "a drastic decline in the number of civilian casualties" because of restrictions imposed by U.S. Gen. Stanley McChrystal, who took command of NATO and U.S. forces last month.

McChrystal ordered troops to limit the use of airstrikes and avoid clashes that could lead to civilian deaths.

"It is our clear intention to do everything possible to reduce the number of civilian casualties to an absolute minimum," Fogh Rasmussen said.

The U.S. military said helicopters had opened fire with guns and rockets and killed four insurgents near Kandahar after spotting them carrying jugs on motorcycles through a field away from a populated area. Spokeswoman Capt. Elizabeth Mathias said the jugs had exploded when hit.

Residents of Kowuk village said three children and a man had been slain. An Associated Press reporter and photographer saw villagers bring the bodies of three boys and a man to the guesthouse of the Kandahar governor, 12 miles south of Kowuk. The angry villagers shouted "Death to America! Death to infidels!" as they displayed the corpses in the back of a pickup truck.

The U.S. said it could not confirm any civilian fatalities, although it was investigating.

Abdur Rahim, the father of the boys and uncle of the slain man from the Kowuk incident, told the AP that he heard a pair of helicopters circling over his compound at 1:30 a.m. Wednesday before they fired two missiles that hit his home. His brother and another son were wounded, he said.

"What was the fault of my innocent children? They were not Taliban," Rahim said. "Did they come here to build our country or kill our innocent children?"

In eastern Afghanistan, a roadside bomb killed two tribal elders and four armed guards Wednesday, said Ahmad Zia Abdulzai, the spokesman for Nangarhar province.

The six were heading to a meeting to discuss road security in the area. Taliban militants regularly use roadside bombs in their attacks against Afghan and foreign troops.