The president said despite having differing opinions on issues, he and Putin have a good professional and personal relationship.
"And how does the relationship work between Mr. Obama and Mr. Biden? They also sometimes speak [about] different things. They even have different backgrounds, different biographies, and probably a different set of opinions about the world and its situation. But it does work," Medvedev said.
In an exclusive interview last week, Obama told Stephanopoulos that he and Medvedev agreed that they should implement sanctions if Iran continues to develop its uranium enrichment program in pursuit of a nuclear weapon.
"I think it's an enormous shift and a signal that Russia, like the United States, recognizes that unless we can get all countries to start abiding by certain rules of the road, and right now, our biggest concerns are obviously Iran and North Korea," Obama said.
Medvedev told Stephanopoulos that the Iranian nuclear program is not transparent and must be carefully monitored. Should sanctions be implemented, Medvedev said, they need to be effective and smart because often they do not work.
"They should not lead to humanitarian catastrophe, where the whole Iranian community would start to hate the whole world," Medvedev said.
The Russian president shot down the notion of a crackdown on Iran's petroleum trade, an idea that many in Congress support.
"If we're talking about energy sanctions, I'll tell you my opinion. I don't think on that topic we have a chance to achieve a consolidated opinion of the global community on that. ... Sanctions should not be paralyzing. They should not cause suffering," Medvedev said.
Last month two female suicide bombers from the Caucasus region killed 40 people in a bombing in the Moscow subway.
Medvedev said it was a "tragic story," calling one woman a child because she was only 17.
"In order to fight such activity, you have to change the psychology of the people. You can create normal life conditions in the Caucasus. You have to destroy all of those who came here for terrorism. Those people are infiltrating through the borders," Medvedev said, referring to terrorists coming from Afghanistan and Pakistan.
Medvedev said Russia faces the same threat the United States does, and said he spoke to Obama about it last week.
"I told him 'Barack, the subways are in many places, and you should take care of the transportation.' This is a huge problem for our countries. And this is not just on the technological level. I'm ready to fully cooperate with our American partners," Medvedev said. "I know our American partners and the president are ready for the same. This is the struggle we'll have for a long time."