Medvedev said neither Russia nor the United States can tolerate "drift and indifference" in their relationship.
Russian-U.S. relations came to a standstill last year amid disputes over U.S. plans to deploy elements of its anti-missile system in Central Europe and Russia's war with Georgia.
The United States remains suspicious of Russia's ties to Iran, while Moscow opposes Washington's drive to grant NATO membership to Ukraine and Georgia.
"I believe that removing such obstacles to good relations would be beneficial to our countries -- essentially removing 'toxic assets' to make good a negative balance sheet," Medvedev wrote.
Medvedev is scheduled to meet U.S. President Barack Obama in London on Wednesday at the G20 summit. He said he was ready to begin rebuilding the relationship at their first meeting.
He said letters he exchanged with Obama earlier this year showed a mutual readiness to build relations in a pragmatic and businesslike manner.
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