BAGRAM AIR FIELD, Afghanistan: The United States accepts that a diminished but resilient Taleban is likely to remain a military threat in some parts of Afghanistan long after US troops complete their combat mission next year, the top US military officer said Sunday.

In an Associated Press interview at this air field north of Kabul, Army Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, said he is cautiously optimistic that the Afghan army will hold its own against the insurgency as Western troops pull back and Afghans assume the lead combat role. He said that by May or June, the Afghans will be in the lead throughout the country.

Asked whether some parts of the country will remain contested by the Taleban, he 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,” he said.

He and other US commanders have said that ultimately the Afghans must reach some sort of political accommodation with the insurgents, and that a reconciliation process needs to be led by Afghans, not Americans. Thus the No. 1 priority for the US military in its final months of combat in Afghanistan is to do all that is possible to boost the strength and confidence of Afghan forces.

Shortly after Dempsey arrived in Afghanistan on Saturday, the Taleban demonstrated its ability to strike.

It claimed responsibility for a suicide car bombing that killed five Americans — three soldiers and two civilians, including Anne Smedinghoff, a foreign service officer and the first American diplomat killed overseas since the terrorist attack Sept. 11 in Benghazi, Libya.

A NATO airstrike Saturday, which came after a joint US-Afghan forced encountered heavy fire from militants during an operation against a Taleban leader, killed 11 Afghan civilians, including 10 children, Afghan officials said.

There are now about 66,000 US troops in Afghanistan. That number is to drop to about 32,000 by February 2014, and the combat mission is to end in December 2014. Whether some number — perhaps 9,000 or 10,000 — remain into 2015 as military trainers and counterinsurgents is yet to be decided.

Dempsey spent two days talking to senior Afghan officials, including his counterpart, Gen. Sher Mohammad Karimi, as well as top US and allied commanders.

He also visited a US base in the volatile eastern province of Paktika for an update on how US troops are balancing the twin missions of advising Afghan forces and withdrawing tons of US equipment as the war effort winds down.

Paktika is an example of a sector of Afghanistan that is likely to face Taleban resistance for years to come.

Bordering areas of Pakistan that provide haven for the Taleban and its affiliated Haqqani network, Paktika has been among the more important insurgent avenues into the Afghan interior.

While the province has a functioning government, Taleban influence remains significant in less populated areas, as it has since US forces first invaded the country more than 11 years ago.