US Defense Secretary Chuck Hagel told American troops on Sunday that he supports a NATO force in Afghanistan after 2014, as Washington and President Hamid Karzai wrangle over a stalled security pact.

Hagel travelled to bases in south Afghanistan to meet troops a day after further tensions arose over the Bilateral Security Agreement (BSA), which would allow some NATO forces to stay in the country after most combat troops withdraw next year.

"I believe there is a role for our coalition partners and the United States, but that depends on the Afghan people," Hagel told soldiers in a question-and-answer session at Camp Bastion in Helmand province.

"If the people of Afghanistan want to continue that relationship, then we will."

US commanders were looking at "a new phase for our mission to train, assist, advise and counter-terrorism", he added.

Meetings with Karzai have been customary over the years for Pentagon chiefs, but Hagel had no plans to meet the Afghan president during his weekend visit.

On a stop in Kandahar on Sunday, Hagel acknowledged "uncertainty about what happens next" for NATO forces after 2014.

"I have hope that the BSA will get signed," he said.

Since President Barack Obama's National Security Adviser Susan Rice and top diplomat John Kerry had already had frank discussions with Karzai urging him to sign the security agreement, Hagel said on Saturday there was no point in him repeating the US position.

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

Hagel did meet the Afghan defence minister, Bismillah Khan Mohammadi, who assured him the security agreement would be signed in "a timely manner".

Karzai, who visited Iran on Sunday, initially endorsed the security pact but has since refused to sign and issued fresh demands.

The agreement sets the legal conditions to permit US and other forces to operate in the country beyond 2014.

Karzai has said the signature could take place after the presidential election in April, but Hagel said that would push the timeline into mid-2014 since the polls are expected to result in a run-off vote.

Eventually there will be "a cut-off point" to cancel a post-2014 mission, he said on Saturday, adding that he was "not prepared to give a date on that".

He said a meeting of NATO defence ministers in February would be crucial for military planners and governments, "and some answers are going to be required at that NATO ministerial".

There are currently 46,000 US 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.

With the long war in Afghanistan often overlooked in the US and Europe, Hagel told US soldiers on Sunday that they were not forgotten.

"I know more than occasionally you wonder if anybody is paying attention, whether anybody cares," he said. "But we do. Our country cares, we do know what you're doing.

"And we appreciate it, very much."

Under a proposed post-2014 mission, roughly 12,000 troops -- mostly American -- would remain in the country to train Afghans and counter Al-Qaeda-linked militants.

In 2011 the US withdrew all its forces from Iraq when it failed to secure a similar troop status accord.