MOSCOW -- President Obama acknowledged Tuesday that Russian Prime Minister Vladimir Putin still casts a long shadow in his country, but dismissed suggestions that Russian President Dmitry Medvedev is little more than a Putin prop. 

"I think that President Medvedev is my counterpart, the president of Russia," Obama said in an interview with FOX News Tuesday. "The prime minister, who I just met today, obviously still has enormous influence." 

The U.S. president said that Medvedev and Putin are on the same page about Russian affairs, even if some think Putin is the master puppeteer controlling the president. 

"Interestingly, nothing Putin said contradicted anything that Medvedev has said," Obama said. "Russia is still in a transition period. It's still growing, still coming out of some of the legacies of the past."

Obama talked about his impressions of Putin, a man he met for the first time on Tuesday in Moscow during a one-on-one meeting. The body language between the two leaders seemed cold on Tuesday, perhaps due in part to an interview the president gave before departing for the trip, in which he said Putin should leave behind the politics of the Cold War.

Obama didn't retract that statement Tuesday, but he did say meeting Putin led him to understand more about the man.

"I think he would admit that his formative years were shaped in the Cold War," Obama said. "Some of his continued grievances with respect to the West are still dated in some of the suspicions that came out of that period."

The topics at the meeting mirrored what Obama discussed with Medvedev on Monday, including missile defense, however Obama and Putin also discussed a contradiction they have over Georgia, a nation anxious to join NATO and a recent source of conflict for Russia.

"On areas where we disagree, like Georgia, I don't anticipate a meeting of the minds anytime soon," Obama said. But he added there's room to work. 

"On areas where we have common interests, like fighting terrorism, I think that there is great potential for us to do some work together," he said. 

Obama also discussed Georgia at a speech earlier in the day at the New Economic School. The president strongly urged Russia to allow state sovereignty for all nations, including Georgia and Ukraine.

"Just as all states should have the right to choose their leaders, states must have the right to borders that are secure, and to their own foreign policies. That is true for Russia, just as it is true for the United States. Any system that cedes those rights will lead to anarchy. That's why we must apply this principle to all nations," Obama said. He also made it clear that NATO wants to work with Russia and not against the country. 

"For any country to become a member of an organization like NATO, for example, a majority of its people must choose to -- they must undertake reforms, they must be able to contribute to the Alliance's mission. And let me be clear: NATO should be seeking collaboration with Russia, not confrontation," Obama said.

Obama rounds out his day Tuesday with a lunch with Medvedev and then a series of meetings with opposition groups in Russia. He heads to L'Aquila, Italy, on Wednesday for the start of the G8 summit. 

Click here to read the transcript of FOX News' interview with Obama.