He also said Russia welcomed U.S. President Barack Obama's plans to review U.S. policy in the war-ravaged Central Asian state.
"We hope the new U.S. administration will have greater success than the previous one in resolving the Afghanistan issue," Medvedev said during the second day of his two-day visit to Uzbekistan.
"Naturally, we are ready for full-fledged, full-format cooperation with all countries on the issue of the provision of security in Afghanistan, including the United States," he also said referring to joint efforts to fight drug trafficking. He also said Russia would work with NATO on transit routes for the delivery of goods into Afghanistan.
Uzbek President Islam Karimov also expressed his country's support for Obama's plans to solve Afghanistan's mounting problems, but said it was too early to assess them. Obama has proposed sending troops from Iraq to Afghanistan to tackle the revitalized Taliban movement.
He also suggested that all the countries in the region should be involved in attempts to bring peace to Afghanistan.
Moscow agreed before last August's war with Georgia to permit non-military NATO supplies to be transferred to Afghanistan across its territory. This meant that deliveries could avoid dangerous parts of Pakistan.
The NATO-Russia Council is expected to hold its first meeting since August's conflict next week. Relations between Russia and the military alliance were frozen after the five-day war, which began when Georgian forces attacked the rebel republic of South Ossetia in an attempt to bring it under central control.