Mitt Romney gave his most expansive answer yet over questions about his tax returns, telling reporters Thursday he has "never paid less than 13 percent" in taxes over the last 10 years -- contrary to what Senate Democratic Leader Harry Reid has claimed.

"I did go back and look at my taxes," Romney said during a news conference at a South Carolina airport. "And over the past 10 years, I never paid less than 13 percent. I think the most recent year is 13.6 (percent) or something like that."

The response follows months of calls for him to release his returns, including from some top Republicans. However, he has declined to make them public, saying it could give his opponents "more ammunition" against him.

Romney had some choice words Thursday for Reid, calling the accusation by him that Romney didn't pay taxes for a decade "totally false."

"I'm sure waiting for Harry to put up who it was that told him what he says they told him," Romney challenged. "I don't believe it for a minute, by the way."

Reid has not released any proof of his claim beyond saying he heard it from an anonymous source. Romney also scolded the press for their "fascination" with the issue, "given the challenges that America faces" -- high unemployment, millions in poverty and a potentially nuclear Iran.

The Obama campaign, which has spent months publicly shaming Romney for not releasing his returns, had one message for the candidate Thursday -- "prove it."

"Given Mitt Romney's secrecy about his returns, coupled with the revelations in just the one return we have seen to date and the inconsistencies between this one return and his other financial disclosures, he has forfeited the right to have us take him just at his word," Obama campaign spokesperson Lis Smith emailed in a statement.

Reid's office reportedly released a statement likewise calling on Romney to prove his claim by releasing the documents.

Meanwhile, the two campaigns continued to spar Thursday over everything from Medicare to a recent gaffe by Vice President Biden.

Biden said earlier in the week that Republicans wanting to deregulate the financial industry are "going to put y'all back in chains," interpreted by some as a racially charged comment.

Paul Ryan fired back on Fox News Radio, calling the comment the mark of a "desperate" campaign, after Romney took sharp exception to the remarks during a Tuesday evening speech.

White House Press Secretary Jay Carney suggested at Thursday's briefing that the Romney campaign is drawing attention to the issue because "that side is losing the policy debate."

Romney, though, used a brief press conference Thursday to deal with policy issues -- namely, Medicare.

Romney, using a dry-erase board, sketched out what he claimed were the differences between the GOP plan and Obama's. Obama's, he wrote, cuts $716 billion from Medicare. The Romney plan, he wrote, includes "no change."

"I know there's an effort by some people to try and bring as much confusion to the topic of Medicare as possible, but I want to bring as much clarity as possible," Romney said.

Ryan's plan technically includes the same Medicare cuts, but Romney and Ryan say they want to repeal the health care law that triggers them.

Obama and his surrogates have likewise hammered the Medicare issue on the stump and in briefing rooms. They claim Ryan's plan to offer government payments to some Medicare seniors a decade from now "ends Medicare as we know it," and claim to have improved the system through the health care law.

Carney also said Thursday that the discussion shows they're focused on "incredibly important substantive issues" despite charges that the campaign and its backers have lately debased the campaign trail rhetoric.