KABUL, Afghanistan — A NATO-led international force is set to expand and will be ready to assume responsibility for security across all of Afghanistan by the end of next year, freeing up many of the 17,600 American troops battling militants here, a NATO general said yesterday.

The announcement follows a surge in fighting between American-led forces and Taliban rebels ahead of elections next month. The bloodshed has led the military to rush in an airborne infantry battalion of about 700 troops on standby in Fort Bragg, N.C.

Yesterday,a roadside bomb exploded near an American military vehicle in eastern Afghanistan, killing an American service member and wounding another as well as an Afghan soldier, an American military statement said.

Washington has long urged NATO to move forward with a plan to expand its 10,000-strong force into Afghanistan’s volatile south and east.

“We are in a position that we can take over the responsibility for all of Afghanistan in the course of the next year,” General Gerhard Back, who oversees the International Security Assistance Force mission from his base in Brunssum, the Netherlands, said.

He said he expects the deployment of extra NATO forces to relieve a “substantial” number of troops from the American-led coalition, which also includes about 3,100 soldiers from 19 other nations.

General Back said NATO troops would need “more robust” rules of engagement, which govern when and how forces can engage the insurgents.

He spoke to reporters after a ceremony marking the change of the command of ISAF, the NATO-led force, from a Turkish general to Italian Lieutenant General Mauro Del Vecchio. The force is made up of troops from 36 nations.

ISAF already maintains security in the capital, Kabul, and the country’s north and west. It plans to increase its size by an unspecified amount and take over in the violence-wracked south from the American-led coalition early next year, before gradually moving into the east.

An ISAF spokesman, Riccardo Cristoni,said most American troops who stay in Afghanistan after NATO takes responsibility for security nationwide would come under NATO command.

But he said it was not clear whether America would also keep a separate force dedicated to hunting Osama bin Laden and other Al Qaeda leaders believed to be hiding along the mountainous Afghan-Pakistani border.

An American military spokeswoman, Lieutenant Cindy Moore, said commanders were still planning how many troops would remain here next year.

Washington has long sought to reduce the number of its troops in Afghanistan. In May, the operational commander of U.S. forces in Afghanistan, Major General Jason Kamiya, said he was optimistic there would be a “modest reduction” this summer — but that has not happened.

NATO has also boosted the size of its force in the past few weeks in response to the violence and in preparation for legislative elections on September 18. It plans to bring in another 2,000 troops before the vote.

Afghan, NATO, and American officials have warned that the spike in fighting may threaten the elections, which is the next key step toward democracy after a quarter-century of war.

The attack that killed the American service member yesterday occurred near a base at Urgun in Paktika province, which borders Pakistan. It came just over a week after two other American service members were killed in separate attacks.