CHARLOTTE, N.C. — President Obama and Mitt Romney sparred over the future of Medicare on Wednesday in a battle to shape public opinion on the proposal by Paul Ryan, Romney's running mate, to revamp the popular health-care program for the elderly and the disabled.

Both sides sought to gain an edge with seniors in Florida and other swing states with large populations of elderly — and perhaps with some younger Americans looking ahead to their retirement.

The rhetoric on what, just days ago, was a marginal topic in the presidential race reflected the impact of Romney's decision to put the Wisconsin congressman on the Republican ticket.

Ryan's Medicare plan is the centerpiece of a proposed federal budget that Republicans in Congress have adopted as their election-year agenda. Romney has said he would sign the Ryan budget into law.

At a campaign fundraiser in Charlotte on Wednesday, Romney told NASCAR team owners and other donors that Obama "cut Medicare funding for current Medicare retirees" to pay for the health-care overhaul.

"That came out of the Medicare trust fund," Romney told supporters at Duke Mansion, a colonial-style banquet hall. "He raided that trust fund to pay for Obamacare. And as seniors hear this, they're going to be angry."

What Romney failed to mention: Obama's $716 billion in cuts in the projected growth of Medicare have no direct effect on the benefits that patients receive. The savings, instead, come from such areas as lower government reimbursement rates for hospitals and nursing homes.

Romney also skirted another nettlesome issue: His running mate's budget proposal relies on the same $716 billion in Medicare cuts. Restoring the cuts, as Romney advocated Wednesday in a CBS interview, would swell the federal deficit in kind. Romney said nothing about how he would cover the expense.

Campaigning in Iowa on Wednesday, Obama said he had not cut benefits for seniors "by a dime." He told a crowd in Dubuque that he had reduced the cost of prescription drugs for seniors and strengthened Medicare overall.

"My plan has already extended Medicare by more than a decade," he said. "Their plan would end Medicare as we know it."

Ryan's proposal, which seeks to minimize political fallout by not taking effect until 10 years from now, would create a system of vouchers for seniors to buy insurance in the private market as an alternative to the current program.

Democrats say, as Obama did in Dubuque, that Ryan's plan "makes seniors pay more so they can give another tax cut to millionaires and billionaires."

Romney praised Ryan's Medicare proposal in his 59-point plan to revive the U.S. economy, saying it "makes important strides in the right direction by keeping the system solvent and introducing market-based dynamics." Romney's Medicare plans would "share those objectives" but differ in unspecified ways, according to his economic proposal.

On "CBS This Morning," anchor Anthony Mason pressed Romney on how he squared Ryan's plan to cut spending on Medicare with his criticism of Obama for making the same reductions.

"First of all, Congressman Ryan has joined my campaign, and his campaign is my campaign now, and we're on exactly the same page," Romney said. "And my campaign has made it very clear: The president's cuts of $716 billon to Medicare; those cuts are to be restored if I become president and Paul Ryan becomes vice president."

Ryan campaigned Wednesday in Oxford, Ohio, on the campus of his alma mater, Miami University.

"Look at your paycheck," he told an enthusiastic crowd of more than 1,000, including much of the current membership of his former fraternity. "Look at the line that shows your payroll taxes. They are supposed to go to two programs, Social Security and Medicare, period. Now because of President Obama they're also going to pay for Obamacare."

Material from The New York Times is included in this report.