KABUL (AP) ― A fierce battle between U.S.-backed Afghan forces and Taliban militants in a remote corner of eastern Afghanistan left nearly 20 people dead, including 11 Afghan children killed in an air strike and an American civilian adviser, officials said Sunday.

The fighting along a main infiltration route from Pakistan on Saturday was indicative of a surge in hostilities as Afghanistan’s spring fighting season gets underway. This year’s will be closely watched because Afghan forces are having to contend with less support from the international military coalition, making it a test case of their ability to take on the country’s resilient insurgency.

The U.S.-led coalition confirmed that it launched air strikes in Kunar province where the deaths occurred, stressing that they were requested by international forces. The coalition said it was assessing the incident, but could not confirm that civilians were killed.

The battle unfolded on Saturday, the same day that a total of six Americans, including three U.S. soldiers, died in violent attacks. In addition to the U.S. adviser killed during the operation in the east, two others ― a female foreign service officer with the U.S. State Department and an employee with the U.S. Defense Department ―died in a suicide bombing in southern Zabul province during a trip to donate books to Afghan students.

The deaths capped one of the bloodiest weeks of the nearly 12-year-old war. On Wednesday, insurgents ambushed a courthouse in the relatively safe west, killing more than 46 people.

The death of Afghan civilians caught in the crossfire has been a major point of contention between international forces and the Afghan government.

Earlier this year, Afghan President Hamid Karzai banned his troops from requesting coalition air strikes.

In the latest incident, Associated Press photos showed villagers gathered for the funerals of the children whose bodies were swaddled in blankets. A garland of flowers adorned the head of a dead baby.

Afghan officials said the air strike occurred after a joint U.S.-Afghan force faced hours of heavy gunfire from militants. The joint force was conducting an operation targeting a senior Taliban leader that began around midnight Friday in the Shultan area of Kunar’s Shigal district, according to tribal elder Gul Pasha, who also is the chief of the local council.

The remote area is one of the main points of entry for Taliban and other insurgents trying to move across the mountainous border from neighboring Pakistan, where they enjoy refuge in the lawless northwestern area.

“In the morning after sunrise, planes appeared in the sky and air strikes started,” Pasha said in a telephone interview, adding that the fighting didn’t end until the evening.

“I don’t think that they knew that all these children and women were in the house because they were under attack from the house and they were shooting at the house,” he said.

There were slightly differing accounts of the death toll.

Pasha said the main Taliban suspect was in the house that was hit and was killed along with a woman and the children, ages 1 to 12, who were members of the suspect’s family.

Provincial government spokesman Wasifullah Wasify said 10 children and one woman were killed and five women, who also were in the house, were wounded.

Karzai’s office later said 11 people were killed --- all of them children -- and six women were wounded.

“While the president strongly condemns the Taliban act of using people and their houses as shields, he also strongly condemns any operation on populated areas that results in civilian casualties,” his office said in a statement.

An air strike in the same district in Kunar that killed 10 civilians in mid-February prompted Karzai to ban his forces from requesting air strikes.

Afghanistan’s Interior Ministry said six Taliban militants were killed in the operation in Sano Dara Sheltan village, including two senior commanders identified as Ali Khan and Gul Raof, the main planner and organizer of attacks in the area.

The U.S.-led coalition said it provided fire support from the air, killing several insurgents.

“The air support was called in by coalition forces, not Afghan security forces, and was used to engage insurgent forces in areas away from structures, according to our reporting,” coalition spokesman Maj. Adam Wojack said in a statement.

He said the coalition takes all reports of civilian casualties seriously, and was currently assessing the incident.

Afghan forces have been increasingly taking the lead in combat operations as international forces move to complete their withdrawal by the end of 2014. But U.S. and other foreign troops still face dangers as they try to clear areas of insurgents and prepare the Afghans to take control.

Gen. Martin Dempsey, the top U.S. military officer, told the AP in an interview on Sunday in Afghanistan that he was cautiously optimistic about the final stage of handing off security responsibility to Afghan forces.

Asked if he thought that some parts of Afghanistan will be contested by the Taliban in 2015, Dempsey replied, “Yes, of course there will be. And if we were having this conversation 10 years from now, I suspect there would (still) be contested areas because the history of Afghanistan suggests that there will always be contested areas.”

There are about 100,000 international troops currently in Afghanistan, including 66,000 from the United States. The U.S. troop total is scheduled to drop to about 32,000 by early next year. The bulk of the decline is to occur after fighting winds down this winter.