Obama said that the new disarmament treaty signed today is "only a start."
"We're looking at a timetable over a five, 10, 15, 20 year time horizon," he said. "We're going to have to continually build and evolve a whole approach that is designed for the 21st century as opposed to the 20th century."
The U.S. plans for a missile defense system still remain a key sticking point between the two nations and Medvedev warned once again that the Russians could pull out from the treaty if they felt it undermined the new foundation of arms control.
Obama disputed that notion to Stephanopoulos and said the Russians are not saying they would withdraw from the treaty over the missile defense system.
"We were firm, and are now absolutely confident that this in no way impedes our ability to move forward on the missile defense program, that's designed not to target Russia," he said in the ABC News interview.
Obama said in remarks in Prague that his administration's plans are not aimed at changing the "strategic balance" with Russia but instead were established with the goal of "protecting the American people" from missile attacks from other nations.
The White House said its work with the Senate will begin immediately and its expectation is that the Senate will sign off on the treaty this year.
"We are hopeful that reducing the threat of nuclear weapons remains a priority for both parties," Gibbs told reporters on Air Force One en route to Prague. "I think it's the president's hope and expectation the Senate will ratify this, this year."
Starting today, administration officials will begin briefing members of the Senate on the specifics of the treaty.
The Russian parliament, the Duma, also needs to sign off on the new disarmament treaty.
ABC News' Jake Tapper, Yunji de Nies and Sunlen Miller contributed to this report.