Dmitry Rogozin's statement came after the 26-nation military alliance decided on Tuesday to resume informal contacts with Moscow.
"NATO is, in essence, taking a step toward Russia, and it would be irresponsible and reckless to ignore that," Rogozin told reporters.
He said, however, that at future talks Russia would "not pretend" that NATO had not backed "the Saakashvili regime" during the August conflict, which began when Georgian forces attacked breakaway South Ossetia.
NATO called Russia's military response to the attack on the rebel republic, whose residents have had Russian citizenship for a number of years "disproportionate." It also condemned Russia's decision to recognize South Ossetia and Abkhazia, another breakaway province, as independent states in late August.
Rogozin also said Russia looked forward to dialogue with Georgia's eventual new leaders, but not its current president, Mikheil Saakashvili, who he implied was in need of psychiatric advice.
"We are ready to talk to Georgia's new political leadership," he said. "And Saakashvili should talk to a doctor."
Russia and Georgia presently have no diplomatic ties.
Speaking after a meeting of NATO foreign ministers on Tuesday, Secretary General Jaap de Hoop Scheffer said: "The allies agreed on what I would qualify as a conditional and graduated reengagement with Russia."
Rogozin earlier said an informal NATO-Russia Council meeting could be held before the end of this month.
