US President Barack Obama has invited Afghan President Hamid Karzai to Washington in January for talks on the future of Afghanistan once NATO-led forces withdraw in two years, officials said.

US Defense Secretary Leon Panetta announced the visit late on Thursday at a joint news conference with Karzai in the Afghan capital Kabul.

Obama had asked his Afghan counterpart to meet him in the United States for talks on January 7 "to discuss a shared vision of Afghanistan beyond 2014," said Panetta, adding that Karzai had accept the invitation.

The Pentagon chief was in Afghanistan for a two-day tour as Obama weighs the pace of a troop drawdown and the size of a potential follow-on force once the bulk of the NATO-led contingent pulls out in 2014.

Earlier on Thursday a suicide car bomber attacked a NATO base in Kandahar, southern Afghanistan, just hours after a visit by Panetta, killing an American soldier and two civilians. Taliban insurgents claimed responsibility for the attack in a text message to AFP.

"America will not turn away from Afghanistan. We will continue to have an enduring presence beyond 2014," Panetta said.

The US military currently has about 66,000 troops on the ground, as part of a NATO-led force of roughly 100,000.

US and Afghan officials have launched negotiations on an accord that would set the terms for a smaller American force after 2014, which would focus mainly on countering remnants of Al-Qaeda in the country.

US administration officials say Obama is considering a possible post-2014 mission ranging from 6,000 to 15,000 troops, if Kabul agrees.

Karzai reiterated his view Thursday that Kabul could be willing to grant legal immunity to US troops in return for the United States helping arm the Afghan military and turning over control of all detainees held by American forces.