GREER, S.C. – Republican presidential candidate Mitt Romney said Thursday that he has never paid less than 13 percent of his income in taxes during the past decade.

But he declined anew to release the records that would prove it.

“I did go back and look at my taxes, and over the past 10 years I never paid less than 13 percent. I think the most recent year is 13.6 or something like that. So I paid taxes every single year,” Romney told reporters after landing in South Carolina for a fundraiser.

Romney has released his 2010 tax return and has pledged to release his 2011 return before the Nov. 6 election, but he has refused to release returns from earlier years.

Democratic Senate Majority Leader Harry Reid, citing an anonymous source, has charged that Romney didn’t want to release any more of his returns because the Republican candidate had paid no taxes in some years.

“Harry Reid’s charge is totally false. I’m sure waiting for Harry to put up who it was that told him what he says they told him,” Romney said.

President Obama’s campaign spokeswoman, Lis Smith, responded by telling Romney to prove it. “He has forfeited the right to have us take him just at his word,” Smith said.

Romney commented as his campaign worked to stay on the offensive in the increasingly heated debate over the future of Medicare, the health care program relied upon by millions of seniors.

“Which of these two do you think is better?” Romney asked as he stood next to a whiteboard comparing his Medicare plan with Obama’s.

“The president was talking about Medicare yesterday. I’m excited about this,” Romney’s running mate, Paul Ryan, said Thursday during an appearance in Ohio.

“This is a debate we want to have, this is a debate we need to have and this is a debate we’re going to win.”

The Wisconsin congressman’s addition to the GOP ticket this past weekend drew immediate scrutiny to a budget proposal he drafted that proposes to transform Medicare into a voucher-like system for future retirees.

In turn, Romney and Ryan called attention to Obama’s health care law, which is funded in part by future savings from Medicare, and accused him of “raiding” the program of billions of dollars.

Obama, a Democrat, says the Republicans’ proposal “ends Medicare as we know it.” He argues that changes he’s made, including to help seniors pay less for drugs and reduce wasteful spending, will make the program stronger financially.

“I’ve strengthened Medicare,” Obama declared Wednesday at campaign events in Iowa.