Evan Vucci/Associated Press

Mitt Romney said on Thursday that he had not paid less than 13 percent of his income in taxes during the past decade, but he called the continued focus on his personal tax returns “small-minded” in the face of the nation’s problems.

Speaking to reporters during a stop in South Carolina, Mr. Romney said that he had examined the last 10 years of his tax returns.

“Every year, I’ve paid at least 13 percent,” he said, apparently referring to his effective federal income tax rate.

Mr. Romney’s decision to address the tax question on Thursday appeared to be the campaign’s latest attempt to put the nettlesome issue of his tax returns behind him. But Democrats seized on the comments as a way to revive the issue and to once again demand proof of his claims.

His statement is the first direct response to attacks by the Obama campaign and its Democratic allies suggesting that Mr. Romney paid little or no taxes in previous years.

In particular, Senator Harry Reid of Nevada has alleged — without any proof — that Mr. Romney paid no taxes in some years, presumably by using offshore tax shelters and other legal accounting measures. Mr. Romney had already denounced that as false.

But Mr. Romney has steadfastly refused to release more than the single year of returns that he has already disclosed. He has released the full returns for the 2010 tax year and a short summary of the taxes he paid in 2011.

In an interview during his trip abroad last month, Mr. Romney was asked whether he had ever paid a tax rate lower than the 13.9 percent he paid in 2010.

“I haven’t calculated that,” Mr. Romney told David Muir of ABC News. “I’m happy to go back and look, but my view is I’ve paid all the taxes required by law.”

Reporters have pressed Mr. Romney and his campaign to follow through on that offer but had been rebuffed. The campaign has continued to insist that Mr. Romney has released all the tax returns he needs to.

Lis Smith, a spokeswoman for the Obama campaign, said that since there was “substantial reason” to doubt Mr. Romney’s claims, “we have a simple message for him: prove it.”

“Given Mitt Romney’s secrecy about his returns,” she said, “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.”

David Axelrod, a senior adviser to Mr. Obama’s campaign, scoffed at Mr. Romney’s statement.

“The ‘trust me, everything’s fine’ approach?” Mr. Axelrod said in an e-mail. “He still can’t answer the basic question: Why not simply do what is the norm — the standard his father set — and release his returns for years back? The argument that he doesn’t want to because his opponents might make something of them is not terribly reassuring.”

In an interview on NBC’s “Rock Center,” Ann Romney said this week that releasing additional tax returns would simply provide “ammunition” for Democrats to attack her and her husband.

“The more we get attacked, the more we get questioned, the more we get pushed,” Mrs. Romney said. She added that she and her husband had been “very transparent to what’s legally required of us.”

“There’s going to be no more tax releases given,” Mrs. Romney said. She added: “Mitt is honest. His integrity is just golden.”

Mr. Romney and his campaign have repeatedly said that he does not want to provide more years of tax returns because Democrats will use the information for unfair attacks on his personal wealth.

Mrs. Romney echoed that sentiment during the interview Wednesday night.

“We pay our taxes,” Mrs. Romney said. “We are absolutely — beyond paying our taxes, we also give 10 percent of our income to charity, so that you know, we have no issues that way and the only reason we don’t disclose any more is, you know, we just become a bigger target.”

In the brief exchange with reporters in South Carolina, Mr. Romney responded to a question about his taxes by expressing disappointment about the continued focus on his own financial situation.

“I just have to say, given the challenges that America faces – 23 million people out of work, Iran about to become nuclear, one out of six Americans in poverty – the fascination with taxes I’ve paid I find to be very small-minded compared to the broad issues that we face,” he said.

But Mr. Romney was clearly ready to use the opportunity to talk about the tax rate that he had paid and to attack Mr. Reid’s allegations.

“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,” Mr. Romney said. “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.”

Mr. Romney’s comments about taxes came after he fielded several questions about his new running mate, Representative Paul D. Ryan of Wisconsin, and the issue of Medicare.

Mr. Romney said he was eager to have a Medicare debate with Mr. Obama and the Democrats.

“I think we’re the ones that brought up the topic,” Mr. Romney said, standing next to a whiteboard on which he sketched out what he said were the differences between the two candidates on Medicare.

“I want to make sure that people understand what the president has done in welfare, what the president has done on Medicare,” Mr. Romney said.

Writing on the dry-erase board with a black marker, Mr. Romney alleged that the president had cut $716 billion out of the Medicare program, saying that the cuts were made “not to save it.”

“It’s not just that he’s cutting $716 billion to make it solvent,” Mr. Romney said. “He cut $716 billion to fund Obamacare.”

Jeff Zeleny contributed reporting.