KABUL - Vice President Biden on Tuesday pledged long-term American support for Afghanistan, offering a commitment to help the war-torn nation beyond the 2014 target both countries have set to have Afghans fully in charge of their own security.

The day after he arrived on an unannounced visit to Kabul, Biden toured a training academy for Afghan soldiers, had lunch with President Hamid Karzai and said he was confident of the effectiveness of the United States' counter-insurgency strategy.

"We've largely arrested the Taliban momentum here in some very important areas," Biden said alongside Karzai. "But these gains, as you pointed out to me Mr. President, we know are fragile and reversible."

During the intense Washington debate leading up to the sending of 30,000 new U.S. troops to Afghanistan, Biden urged a smaller U.S. military footprint more focused on counterterrorism operations against Al Qaeda and Taliban leaders.

"It is not our intention to govern or to nation-build," Biden said. "As President Karzai often points out, this is the responsibility of the Afghan people, and they are fully capable of it."

But he stressed that the United States will continue to assist the Afghan government.

"If the Afghan people want it, we won't leave in 2014," Biden said.

Biden flew into Kabul on Monday night to assess the progress of the decade-long war against the Taliban and determine whether Afghan troops are ready to start taking over from their American allies.

After touching down at Kabul airport on a cold and overcast evening, Biden was greeted by U.S. Ambassador Karl W. Eikenberry and the American military commander, Gen. David H. Petraeus, along with Afghan officials.

The main purpose of the trip, according to a White House official, was to "assess progress toward the transition to Afghan-led security beginning in 2011." With American troops slogging it out against the Taliban, many officials expect little change in the U.S. military presence this year.

Biden's visit, his first since taking office, brings him to the Afghan capital at a time of uncertainty in the war. Military commanders claim progress against the Taliban in the areas where they've concentrated U.S. troops, particularly in the southern Afghan provinces of Kandahar and Helmand. And President Obama last month called the war effort "on track."

But the insurgency remains potent in wide swaths of the country. The Afghan government has strongly opposed parts of the U.S. military strategy and has not yet addressed its own problems with corruption. Insurgent leaders, meanwhile, operate safely from sanctuaries in Pakistan.