The two leaders, attending the two-day Nuclear Security Summit in Seoul, held their last official meeting before Russian President-elect Vladimir Putin takes office in May. The conversation was picked up by the microphones as reporters were entering the room for remarks by Obama and Medvedev at the end of their meeting.
Republicans in Congress have accused Obama of seeking a deal with Russia that would not stand up to electoral scrutiny -- a view shared by the two presidential contenders.
"That is an alarming and troubling development," said Romney, calling the president's comment "revealing" for what he called Obama's unwillingness to provide more details about missile defense.
"This is no time for our president to be pulling his punches with the American people," Romney said while campaigning in San Diego. "I will make it very clear that the relationship we have around the world is one where America will be strong, that America's strength and commitment to our friends and allies will be unshakable and unwavering."
Gingrich called the exchange with Medvedev an "extraordinary moment caught on tape where the president basically said to a Russian leader, 'Please wait until after the election so I can sell out.'
"If you read what he said, it is the most blatant comment about selling out American defenses I think any American president's ever made and I don't see how any American could trust him ever again after that comment," Gingrich said. "I mean, he thinks it's in private and he's saying to the Russians, please quote 'give me some space' so I can be re-elected and then I'll be free to do anything I want to. Well, that just told you how radically left-wing Obama's going to be in the second term."
The Obama campaign was quick to respond to Romney's comment, saying that he had undermined his own credibility by speaking so flippantly.
"Governor Romney has been all over the map on the key foreign policy challenges facing our nation today, offering a lot of chest thumping and empty rhetoric with no concrete plans to enhance our security or strengthen our alliances," Obama 2012 press secratary Ben LaBolt said in a statement.
"Governor Romney once said that a president is not a foreign-policy expert and that he would rely on the experts and defer to his lawyers on critical foreign policy issues. Instead of passing the buck, it is time that Governor Romney shared his foreign policy agenda with the American people."