"I am convinced that without addressing all of our concerns in a frank and fair way we will be unable to make any headway in building a Greater Europe," he said, speaking in Berlin after talks with Chancellor Angela Merkel during his first European trip since being sworn into office on May 7
He also added that "organizations operating in the Euro-Atlantic region" could also join it.
He said a new security arrangement should be based on "pure" national interests, not skewed by ideological motives.
The president also said that without cuts in military spending it would be impossible to raise sufficient resources to deal with such global challenges as climate change, illegal migration, and global poverty.
He also said that NATO's further eastward expansion would harm the bloc's relations with Russia, but there would be no confrontation.
Medvedev urged NATO to halt its enlargement and missile defense plans in Europe, adding that it was critical to break the vicious circle of unilateral actions.
He also said earlier on Thursday that Russia was alarmed by "narrowing trends of mutual understanding in Euro-Atlantic policies."
Russia and the EU are to start talks on a new wide-reaching strategic partnership agreement at a summit later this month.
