Speaking on NBC's "The Tonight Show" with host Jay Leno, Obama said Moscow sometimes slipped into a Cold War mentality.
He did not mention whether he would attend a separate one-on-one meeting with Russian President Vladimir Putin. The White House has said it is evaluating whether that meeting makes sense.
"What I say to President Putin is, that's the past and ... we've got to think about the future. And there's no reason why we shouldn't be able to cooperate more effectively than we do."
Asked whether the controversial surveillance programs helped lead to the intelligence that sparked the warnings, Obama said the programs were critical to counterterrorism work. But he said more needed to be done to assure Americans they were not being spied on themselves.
"We don't have a domestic spying program," he said. "What we do have are some mechanisms where we can track a phone number or an email address that we know is connected to some sort of terrorist threat."
Obama also said the recent threat that caused the United States to close embassies throughout the Middle East was significant.
"It's significant enough that we're taking every precaution," Obama said.
Voice of Russia, Reuters