RIA Novosti reported Kissinger, who served as secretary of state from 1973-77, said he was honored to meet with Medvedev, who was inaugurated May 7.
"I have followed with great interest your becoming president and the plans you have put forward in some of your speeches. I wish you every success. It is important for Russia and important for the world," Kissinger was quoted as saying.
Kissinger serves as U.S. chairman of the panel "Russia-USA: A Look into the Future," which was formed last year and led by former Russian Prime Minister Yevgeny Primakov.
His visit to the Kremlin comes as U.S.-Russian relations have strained over U.S. plans for a missile shield in Central Europe and Kosovo's declaration of independence from Serbia.