"He is smart, tough, shrewd... he is unsentimental," Mr. Obama said.
"He thinks in terms of what's good for Russia and will pursue interests aggressively, but he also wants to approach U.S.-Russian relations in a pragmatic way," Mr. Obama said.
Mr. Obama's remarks about Putin are being closely watched and compared to those made by former President George W. Bush after he first met with Putin as president in 2001, where he famously said that he trusted him by looking him in the eye and sensing his "soul."
"I looked the man in the eye. I found him to be very straight forward and trustworthy and we had a very good dialogue. I was able to get a sense of his soul," Mr. Bush said then.
Mr. Obama said today that the two countries have common interests on terrorism and potential commercial ties. He also said he found nothing inconsistent between Putin and Russian President Medvedev.
"We disagree on spheres on influence," the president added. "If a country on Russia's border wants to join NATO it's their prerogative."
A White House official told the Associated Press that Mr. Obama and Putin "formed the basis of a good relation" during their meeting. "I would say he's very convinced that the prime minister is a man of today and he's got his eyes firmly on the future," the official told the AP.
Putin, for his part, said the meeting with Mr. Obama went "very well," reports the AP, saying it was "substantive, informative and collaborative" and that they had "many points in common."
You can watch the video above, where the president also talks about efforts to keep Iran and North Korea from having nuclear weapons.