Ryan, chairman of the House Budget Committee, argued that his proposal is not "radical," as Gingrich alleged during an interview over the weekend. And he questioned why Gingrich was choosing to align himself with Democratic critics of the GOP budget proposal.
"With allies like that, who needs the left?" Ryan quipped, during an interview on Laura Ingraham's radio show.
Ryan was in Chicago on Monday to defend his budget outline, which calls for phasing out direct Medicare payments to doctors and hospitals in favor of a system of subsidized private insurance for seniors. Republican leaders in Congress generally have supported the plan, though a handful have indicated it is just a starting point for negotiations. But Gingrich, appearing on NBC's "Meet the Press" just days after announcing his presidential campaign, launched a broadside on the program Sunday.
"I don't think right-wing social engineering is any more desirable than left-wing social engineering. I don't think imposing radical change from the right or the left is a very good way for a free society to operate," he said when asked about Ryan's proposal.
Gingrich called for a "national conversation" on Medicare but described Ryan's proposed overhaul as "too big a jump."
"I'm against Obamacare, which is imposing radical change, and I would be against a conservative imposing radical change," he said.
Ryan agreed that President Obama's health care approach is "radical" but took issue with the rest of that sentence.
"What we're simply saying is don't give the power to a bureaucrat to ration care," Ryan said. "Hardly is that social engineering and radical. What's radical is kicking the can down the road, not doing anything to fix this problem and watching the whole system implode on itself."
Ryan reiterated that his proposal would leave benefits untouched for Americans 55 and older, while giving younger workers a choice of "guaranteed coverage options," offering more government aid to those who are poor, sick or both.
"I mean, that's hardly radical," Ryan said.
Such a proposal, though, is estimated to cost seniors more out of pocket over the long run, leading to charges from Democrats that the Republican budget is unfairly placing the burden for reducing the deficit on the backs of seniors.
House Democratic Leader Nancy Pelosi said last week that the proposal would undermine America's social contract, though she told CNBC on Monday that Medicare is "on the table" in ongoing budget talks.
Though Gingrich has put the Medicare overhaul in his sights, Time magazine reports that Gingrich recently expressed support for the proposal, and for Ryan, during a visit to New Hampshire -- though he described it as a "first step" at the time.
Separately, Gingrich's campaign issued a clarification Monday regarding another comment he made during the "Meet the Press" interview. Asked about the so-called individual mandate in the federal health care overhaul, Gingrich said Sunday he believes "all of us have a responsibility to help pay for health care" and expressed support for "some requirement."
Gingrich, though, said in a statement late Monday that he believes the individual mandate requiring people to buy health insurance is "unconstitutional," and that he is committed to the "complete repeal" of the health care overhaul.
"In a free society you cannot tell citizens what they should buy and what those things should be," he said. "I also believe individuals should be responsible to pay for the care that they receive."