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 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.
Obama campaign 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.
White House spokesman Jay Carney declined to comment on Romney's tax rate. He said Democratic President Barack Obama believes "the tradition for presidential candidates to put forward multiple years of their tax returns is a useful and valuable one. Not always comfortable."
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, added 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 President Barack 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.
"What he probably did not mention yesterday is that when he passed his signature health care achievement, Obamacare, he raided $716 billion from Medicare to pay for Obamacare," Ryan, chairman of the House Budget Committee, said. "This will lead to fewer services for seniors."
What Ryan doesn't mention is that his budget proposal includes the same savings, which are supposed to be realized through lower payments to hospitals and doctors, and by making the program more efficient.
Romney has said he would restore the Medicare cuts.
Obama says the Republicans' proposal "ends Medicare as we know it," arguing 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 separate campaign appearances in Iowa.
The Medicare debate continues as Romney's campaign also presses ahead with efforts to undermine Obama's personal likability, one of his greatest assets, by trying to portray the outwardly calm president as someone seething with animosity and a lust for power.
Ryan carried the theme in his only public appearance Thursday, his second consecutive day of campaigning in the politically important state of Ohio. He said Obama was running a campaign marked by "frustration" and "anger" because he's out of new ideas and has resorted to "fear and smear" to try to win a second term.
Romney had charged a day earlier that "division and attack and hatred" were fueling Obama's campaign.
To help make their case, Romney's campaign has been highlighting a recent remark by Vice President Joe Biden that prompted some critics to suggest he was using racial undertones to gain political advantage.
Responding to Republican criticism that the Obama administration had sought to regulate Wall Street too tightly, Biden told a Virginia campaign audience that included hundreds of black supporters that the GOP wanted to "unchain Wall Street." He added: "They're going to put y'all back in chains."
Obama defended Biden, telling People magazine Wednesday that the vice president's only meaning was that consumers won't be protected if Wall Street reforms are repealed.
"In no sense was he trying to connote something other than that," Obama said.
The president wrapped up a three-day bus tour through Iowa on Wednesday, devoting attention to the state that helped launch his bid for the White House in 2008. He was joined by first lady Michelle Obama for the first time in months.
Romney was raising money in South Carolina.
Obama resumes campaigning Saturday with a pair of stops in New Hampshire.