The president said that discussions will continue to move forward, as part of which Medvedev will visit the United States this summer.
Medvedev said "at present' the language within the treaty signed "satisfies both parties" but indicated that he still hoped a compromise on this issue could be reached between the two countries.
Obama also faces resistance from some members of the U.S. Senate, who have to ratify the treaty. The agreement requires the signature of 67 senators to be ratified, which means Obama will need bipartisan support. But some Republicans argue that the agreement endangers and restricts the U.S. missile defense program. Others say the idea of a world free of nuclear arms -- a vision that the president has spoken about repeatedly since he took office -- is simply utopian.
The White House says they will begin working with the Senate to ratify this treaty immediately, with the expectation that it will be ratified this year.
"We will spend a lot of time, and our team will spend a lot of time meeting with individual senators and individual senator's staffs over the next many months to make this happen," White House press secretary Robert Gibbs told reporters.
He said earlier, "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 and the White House emphasized that prior arms control treaties have been ratified with huge bipartisan majorities.
Obama expressed confidence that ratification would be achieved by both countries.
"I am actually quite confident that Democrats and Republicans in the United States Senate having reviewed this will see that the United States has preserved its core national security interests, that it is maintaining a safe and secure and effective nuclear deterrent but that we are beginning to once again move forward leaving Cold War behind to address new challenges in new ways," he said.
In Russia also, the treaty needs to be ratified by the Duma, the country's parliament.
Ryabkov told reporters that they "would not hold the Duma hostage" and hope to have ratification by the U.S. midterm elections in November.
Obama went from guest to host this evening in Prague. The president met with 11 leaders from Central and Eastern European for dinner at the ambassador's residence.
The countries attending the dinner were Bulgaria, Croatia, Hungary, Lithuania, Slovenia, Poland, the Slovak Republic, Latvia, Estonia, Romania and the Czech Republic.
White House officials were adamant in rejecting the notion that the dinner was to reassure the Central Europeans that the warming of relations between the United States and Russia will not come at their expense.
"We have been clear cut from day one, from April 1, that as we advance our interest with Russia in seeking mutual cooperation, we're not going to link that to other places as a quid pro quo," McFaul, the president's special assistant, said. "That is simply not a game that we're going to play."
Administration officials said they believe a more substantive relationship with Russia is good for security in this region of the world.
"It's not a zero-sum game. It actually can be beneficial to both," McFaul said.
On the agenda at the meeting were wide-ranging issues including the global economy, European security and Afghanistan. Medvedev was not present at the meeting.