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The Afghan and US presidents are to meet in January to discuss the US troop presence after 2014, US Defence Secretary Leon Panetta said Thursday in Kabul.

A suicide bomber targeted the second-largest US military airfield in the southern province of Kandahar just hours before Panetta visited it.

On the second day of his unannounced visit to Afghanistan, Panetta met President Hamid Karzai to talk about the withdrawal.

"The United States ... has issued a formal invitation to President Karzai from President Obama to meet in Washington during the week of January 7 to discuss a shared vision of Afghanistan beyond 2014," Panetta told a joint press conference.

Karzai said he will discuss with Obama the number of US soldiers his government would want in the country after 2014. "We will be discussing this issue and all other relevant issues in Washington and then the proper announcement will be made," he said.

Detainees and US-run detention centres were important issues for Afghanistan, Karzai said, before it signs any security agreement with the United States.

The two countries are currently negotiating an agreement on the role of US troops after 2014, including the number of troops and bases.

One of the major issues is immunity for US troops if they violate Afghan law.

Karzai last week said he was willing to consider immunity for US soldiers if his demands concerning Afghanistan's sovereignty were respected.

These include the handover of all detainees, shutting down of all US prisons in the country, handover control of Afghan airspace, and stopping military raids on villages.

The US has more than 65,000 soldiers in Afghanistan, along with about 30,000 NATO troops.

Panetta praised the country's security forces and said Afghanistan was moving towards the "right direction in achieving sovereignty and independence".

"The ANSF (Afghan national security forces) are out in the frontlines as we speak fighting and dying every day to protect their fellow citizens. Afghans now represent more than two-thirds of those serving in uniform in this country," Panetta said.

"There were many questions, about whether the Afghan forces are ready to step up, but they have taken the lead for providing security in more than 75 per cent of the Afghan population," he added.

One US soldier and two Afghan civilians were killed and 18 Afghans and three US troops were wounded in the Kandahar suicide attack, the provincial governor's office said.

Earlier, an official at the Afghan army hospital in Kandahar had said they had received four bodies.