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"We are still at war," said Mr. Hagel, who earned two Purple Hearts while serving as a combat infantryman in Vietnam.

Before landing in the Afghan capital, Mr. Hagel said a significant focus of his visit would be assessing the detailed plans for transferring responsibility for security to the central government, army and the police here by the time the NATO combat mission expires in December 2014.

"That transition has to be done right," Mr. Hagel said. "It has to be done in partnership with the Afghans, with our allies." He emphasized the importance of "our continued focus and energy and attention on Afghanistan" even as the number of American troops sharply declines.

Mr. Hagel has visited Afghanistan four times before, while serving as a Republican senator from Nebraska. His first trip, in January 2002, came just a month after the rout of Al Qaeda fighters and the Taliban government that had provided Osama bin Laden safe haven.

His most recent visit was in July 2008, when he accompanied a Democratic senator from Illinois — Barack Obama, who as president nominated Mr. Hagel to his current post. Since retiring from the Senate in 2009, Mr. Hagel has not been as directly involved in Afghan policy as was his predecessor, Leon E. Panetta, who arrived at the Pentagon from a tour as C.I.A. director.

Given the evolving mission, Mr. Hagel acknowledged that another goal for his visit was "to better understand where we are in Afghanistan" as the American and allied role shifts from combat to a mission focused on training and advising.

"Even as we move into more of a support role, this remains a dangerous and difficult mission," Mr. Hagel said in a separate statement to American and coalition personnel issued upon his arrival. "But the goal we have established — to have Afghans assume full responsibility for security by the end of 2014 — is clear and achievable."

The small American military force that carried out the invasion of Afghanistan, ordered in retaliation for the Sept. 11 terrorist attacks by Al Qaeda, grew to more than 100,000 under Mr. Obama's troop increase. But it has now dropped to 66,000, and by early next year will be cut in half, falling to a planned 32,000.

"I need to talk to, listen to, get a good sense from our commanders on the ground," Mr. Hagel said. The defense secretary also is scheduled to meet with President Hamid Karzai, who has proved to be a complicated partner for the American government as he has grown increasingly assertive.

Mr. Obama has made no decisions on the size of a possible American military presence beyond 2014, and Mr. Hagel said this trip to Afghanistan would put him in a better position to offer advice to the president. NATO defense ministers have discussed proposals for an American and alliance force of between 8,000 and 12,000 troops after 2014, although senior American commanders proposed a somewhat larger combined coalition deployment of up to 20,000 troops.