The Bilateral Security Agreement (BSA) has been at the centre of a public dispute between the allies, with the US increasingly frustrated by President Hamid Karzai's negotiating tactics over the deal.

After meetings in the Afghan capital, Hagel told reporters that Defense Minister Bismillah Khan Mohammadi "assured me the BSA would be signed in a timely manner".

Washington and NATO have repeatedly appealed to Karzai to sign the BSA, which lays out the rules for US-led troops to operate in Afghanistan after 2014 on a mission focused on training and countering Al-Qaeda-linked extremists.

The Afghan president, who will stand down next year after two terms in power, recently refused to sign the pact promptly despite a "loya jirga" national assembly that he convened voting for him to do so.

President Barack Obama's deputies have warned that unless Karzai relents before the end of the year, there will be no option but to prepare for a full US exit -- the so-called "zero option".

The NATO commander in Afghanistan, General Joseph Dunford, said Saturday that he had not started planning for a total US withdrawal but that he would have to within "weeks" without the BSA being signed.

"In some weeks, I expect we'll start to plan for something other than 'Resolute Support'," Dunford told reporters, referring to NATO's current post-2014 plan.

Dunford said the military would have to "look at a couple of different possibilities".

With no US boots on the ground, Afghanistan would face the risk of a Taliban resurgence and likely lose out on a billions of dollars of military and other international aid.

There are currently 46,000 American troops and 27,000 soldiers from other coalition countries in Afghanistan, and almost the entire NATO-led force is scheduled to pull out by the end of next year.

Under the proposed post-2014 mission, roughly 12,000 troops -- mostly American -- would remain in the country, under rules that would allow controversial house raids by NATO forces only in special circumstances.

Washington had initially set an October deadline for clinching the security agreement and later insisted on a signature by the end of this year.

President Karzai's spokesman Aimal Faizi had told AFP that Hagel was due to met with Karzai and have dinner with him, but Faizi later said no meeting would take place.

"I never asked for a meeting with President Karzai," Hagel told reporters. "That was not the purpose of my trip.

"There's not much I can add in a meeting with President Karzai to what's already been said.

"The people of Afghanistan through the body that he empaneled, the loya jirga, spoke rather plainly and clearly and dramatically about the interests for this country going forward."

Hagel said his visit was primarily to thank US soldiers for serving in Afghanistan.

"The United States has made its position on the BSA clear," a senior US defence official told reporters.

"And just two days ago, President Karzai repeated his position to senior US officials that he is not yet ready to sign the BSA and provided no timeline or practical step for doing so."

Faizi said Afghanistan's two sticking points over the BSA were an "absolute end of (US) military operations on Afghan homes" and a "meaningful" launch of a peace process with the Taliban.

"We don't want our people to get killed by US troops again and again," Faizi said in a reference to Afghan anger over civilian casualties.