Reports say the two discussed Rumsfeld's announcement yesterday that the U.S. will reduce its troop strength by between 2,000 and 3,000 soldier from the current 19,000.
Rumsfeld said that: "The United States has recently announced some adjustments in our force levels here from three brigades to two. Of course the U.S. will be continuing our contribution to NATO. We have been deeply involved in NATO since its beginning and of course have been supportive in the NATO involvement in [the International Security Assistance Force]."
Rumsfeld told reporters after the talks that despite its decision to reduce troops, the U.S. will "continue to be focused on rooting out" the remnants of the Taliban and Al-Qaeda.
Karzai said Aghanistan was not concerned the troops cut meant a reduction in the U.S. commitment to the country.
Rumsfeld arrived in Afghanistan earlier today from neighboring Pakistan, where he toured areas devastated by the 8 October earthquake.
The quake killed more than 74,000 people in India and Pakistan.
Announcing the troop reduction, Rumsfeld said it will not have an adverse impact on U.S. military operations in Afghanistan, where U.S. and NATO forces have been based since the Taliban regime was toppled four years ago.
(RFE/RL's Afghan Service/AFP)