Sergei Storchak said Russia is ready to cancel the debt provided the measure "is accompanied by a recognition of the debt" on the part of Afghanistan.
Storchak said that Afghanistan borrowed funds from the Soviet Union but has not recognized the debt nor made any repayments.
He said any agreement on debt cancellation should be free from Afghan claims for reparations and compensation for the presence of Soviet troops on Afghan territory.
The Soviet Union invaded Afghanistan in 1979 to prop up a pro-Moscow communist regime. The occupation ended with the withdrawal of Soviet forces in 1989.
Storchak was speaking on arrival in London on the eve of an international conference on the future development of Afghanistan.
(Interfax, ITAR-TASS, AP)