Updated at 1:40 p.m. ET
(CBS News) After weeks of speculation about his tax returns, Mitt Romney on Thursday said he paid at least 13 percent in income taxes for each of the past 10 years.
"I did go back and look at my taxes, and over the past 10 years I never paid less than 13 percent," Romney told reporters at the Greenville-Spartanburg International airport in South Carolina. "I think the most recent year is 13.6 or something like that. So I paid taxes every single year."
Romney has publicly released his 2010 tax return and an estimate of his 2011 return. He has refused to release any more, arguing that Democrats will use the returns to level false charges against him.
The presumed GOP candidate has come under fire from both Democrats and some Republicans for refusing to release more of his tax returns. Senate Majority Leader Harry Reid said that an "extremely credible" source from Bain Capital -- the private equity firm Romney founded -- told him that .
"Harry Reid's charge is totally false," Romney said today. "I'm sure waiting for Harry to put up who it was that told him what he says they told him. I don't believe it for a minute, by the way. But every year I've paid at least 13 percent, and if you add in addition the amount that goes to charity, why, the number gets well above 20 percent."
Romney's campaign had previously denied the candidate ever paid $0 in taxes, though this is the first time he's offered more specific information about what he's paid in the past. When asked in a July 29 interview with ABC whether he's ever paid a rate below 13.9 percent, Romney said, "I haven't calculated that. I'm happy to go back and look, but my view is I have paid all of the taxes required by law."
Sen. John McCain, whose 2008 presidential campaign reviewed several years of Romney's returns during the vice presidential vetting process, has also said that.
Romney added that given the challenges facing America, "the fascination with taxes I've paid I find to be very small-minded."
The Obama campaign responded to Romney's remarks today with a challenge.
"Mitt Romney today said that he did indeed 'go back and look' at his tax returns and that he never paid less than 13% in taxes in any year over the past decade," Obama campaign spokeswoman Lis Smith said in a statement. "Since there is substantial reason to doubt his claims, we have a simple message for him: prove it. Even though he's invested millions in foreign tax havens, offshore shell corporations, and a Swiss bank account, he's still asking the American people to trust him."Romney also used his short briefing with reporters on the campaign trail to compare his plan for Medicare reform with President Obama's. To help spell out the differences, Romney drew up a chart on a white board.
"I describe in my plan how we keep Medicare solvent," Romney said, adding that his plan focuses on creating greater competition and means testing future Medicare recipients so that higher-income people receive lower benefits.
By contrast he said, Mr. Obama is not cutting funds from Medicare not to keep it solvent, but "to fund Obamacare."