Brussels, Belgium ? The United States would like NATO eventually to take over the military mission in Afghanistan, where an American-dominated force is still hunting down remnants of the Taliban rule that collapsed two years ago, Defense Secretary Donald Rumsfeld said Sunday.

In an interview on the eve of a NATO defense ministers conference, Rumsfeld said he had not proposed such a transition from U.S. control but that it was a goal “we certainly have favored.”

Rumsfeld arrived in Brussels on Sunday for NATO talks on a range of defense and security issues, including the situation in Iraq and the outlook for a realignment of U.S. forces in Europe. The latter topic is focused mainly on ways of reducing or shifting U.S. troops in Europe to make the overall American military more suited to fighting terrorism and other nontraditional threats.

Defense ministers were meeting today and Tuesday, followed by talks among foreign ministers on Thursday and Friday.

Rumsfeld praised NATO for taking a first, limited step: assuming control over the International Security Assistance Force that keeps the peace in Kabul, the Afghan capital, and trying to put together even more troops so the peacekeeping mission can be expanded beyond Kabul to as many as six provincial cities.

That security force has not been involved in the American-led combat missions against Taliban holdouts.

In advance of this week’s NATO talks, alliance officials expressed confidence that plans would proceed for a German-led NATO security force to move into the northern Afghan city of Kunduz within weeks.

That operation is supposed to be a pilot project for a broader NATO plan to provide protection for “provincial reconstruction teams” in other cities — if it can muster the troops.

“I think it’s a good thing,” Rumsfeld said. “And my guess is it will happen.”

He added that NATO involvement eventually might expand even further.

“At some point the task may mature to the point where NATO would want to take on a still larger responsibility,” he said. While the Pentagon chief did not foresee alliance troops replacing U.S. troops entirely, he would not rule out NATO eventually taking primary control of the military mission.

“I’m not predicting anything, but we certainly have favored that, over time,” Rumsfeld said.

The United States has about 10,000 troops in Afghanistan.