KABUL, Afghanistan — International military forces in Afghanistan handed over control of a peaceful province in the center of the country to Afghan police on Sunday, taking another step in a transition that will allow foreign troops to withdraw in full by the end of 2014.

Bamiyan province is one of seven areas going to Afghan security control this month in a first round of the transition. Another, Panjshir province in the east, began being transferred earlier this month. Both places have seen little to no fighting since the overthrow of the Taliban nearly 10 years ago and barely had any coalition troop presence.

Violence has increased in other parts of Afghanistan since the Taliban began a yearly offensive in April. Afghan and NATO troops killed at least 13 Taliban fighters in the east on Sunday, and three NATO service members were killed in roadside bomb attacks.

The transition to Afghan control will allow international military forces to slowly start withdrawing from Afghanistan until all combat troops are gone in just over three years.

Bamiyan only had a small foreign troop contingent from New Zealand. Bamiyan and Panjshir are the only two provinces that will be handed over in their entirety during this month's transition phase.

Other areas to be handed over are the provincial capitals of Lashkar Gah in southern Afghanistan, Herat in the west, Mazer-e-Sharif in the north and Mehterlam in the east. Afghan forces will also take control of all of Kabul province except for the restive Surobi district.

Not all residents of Bamiyan were happy with the handover decision, which they said had resulted in increased violence in the province by insurgents seeking to make the Afghan government look bad.

"From my point of view, but also the point of view of many in Bamiyan, the transition that occurred today was not a good idea at all," said Bamiyan lawmaker Abdul Rahman Shaheedani. "People are very concerned about security in Bamiyan right now. When several months ago they announced the areas where the first phase of transition would occur, and named Bamiyan, militant activities increased."

In Sunday's fighting, Afghan and NATO troops fought an overnight gunbattle with Taliban insurgents and called in an airstrike on the building where the fighters were holed up. At least 13 Taliban were killed.

Capt. Justin Brockhoff, a spokesman for the coalition, said the overnight operation targeted a Taliban leader in the Kuz Kunar district of Nangarhar province. The force of Afghan and coalition troops came under fire and insurgents refused requests to come out of the building, he said.

The fighting ended Sunday with a NATO airstrike, he said, adding that there were no casualties among civilians or security forces. The insurgents were armed with machine guns, assault rifles and rocket-propelled grenades.

"As Afghan members of the security force attempted to clear the building, they were met with continuing insurgent fire," Brockhoff said. The coalition and Afghan forces eventually called in an airstrike, which "killed several more insurgents and destroyed the building," he said.

Ahmad Zia Abdulzai, a spokesman for the Nangarhar provincial governor, said the bodies of 13 insurgents have been found so far. He said the building occupied by the Taliban was a school, which was empty because the students are on summer break.

Also Sunday, NATO said three of its service members died. One was killed by a roadside bomb in eastern Afghanistan and two were killed by a similar device in the south. It did not release their nationalities or any further details. The deaths bring the total number of coalition forces killed this month to 34.

Britain's Ministry of Defense also confirmed that a British soldier had been shot dead in what Afghan officials said was an attack by a gunman in Afghan army uniform on Saturday. The ministry said the soldier from the 9th/12th Royal Lancers was on a joint NATO-Afghan army patrol in Helmand province when he came under small-arms fire.

"A report that the fatal gunshot was fired by an Afghan National Army soldier is now the subject of a joint International Security Assistance Force and Afghan National Security Force investigation," said Lt. Col. Tim Purbrick, a spokesman for British forces in Afghanistan.

The soldier's name was not released but his family has been informed, the ministry said.