WASHINGTON — White House hopeful Mitt Romney offered his fullest explanation yet about his tax status Thursday, saying he paid at least 13 percent a year over the past decade, but President Barack Obama's campaign offered a prompt retort: prove it.

Romney, a multimillionaire former investor, has been under assault by Democrats for refusing to release pre-2010 tax returns, and he appeared irked by the question about his personal finances in the midst of some of the most heated rhetoric of the 2012 campaign.

"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 told reporters at an airport near Greenville, South Carolina.

"But 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," he said.

Romney paid an effective tax rate of 13.9 percent in 2010, according to returns he has released, as his income from investments was taxed as a capital gain rather than under the higher rates applied for salaried income.

Those figures may not sit well with many middle-class Americans who pay a higher rate than Romney because they pay taxes on salaried income more than investment income. The current highest US income tax rate is 35 percent.

Obama's campaign threw down the gauntlet, saying that "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," Obama campaign spokeswoman Lis Smith said in a statement.

"However, 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."

Romney was fighting unsubstantiated accusations by Senate Majority Leader Harry Reid, who charged earlier this month that Romney went 10 years without paying taxes.

"Harry Reid's charge is totally false," Romney said.

Democrats have sought to tar Romney as a wealthy elitist with no sympathy for the common man. He has proposed cutting income tax rates by 20 percent, eliminating tax on investment income, and slashing the corporate tax rate.

Obama has said such a proposal would hike taxes on families with children by $2,000 to pay for his $5 trillion tax plan, which would mostly benefit the wealthy.

Republican Senator Jim DeMint, who introduced Romney at a fundraiser in Greenville, said Democrats would keep hammering away at the tax issue in order to create a distraction.

"They're not going to let it go," DeMint said. "They'll keep harping on it because they don't want to talk about the economy."

This week featured some of the most explosive rhetoric of the campaign, with Vice President Joe Biden warning voters in Virginia, a former slave-owning state, that Romney's Wall Street policies would "put y'all back in chains."

Romney returned fire, saying Obama's campaign was steeped in "hatred" and division.

But White House spokesman Jay Carney said Thursday that Romney's complaint showed the Republican wanted to change the subject because "that side is losing the policy debate" on issues such as Medicare, the government funded health plan for seniors.

Romney has come under scrutiny since selecting congressman Paul Ryan as his running mate. Ryan has backed turning some of the popular plan into a voucher system in order to cut costs -- a move Democrats say would shred Medicare.

Republican leaders have hailed Ryan as a huge shot in the arm for the Romney campaign, but the first major polls since the announcement showed no appreciable bump.

Before the blizzard of media coverage unleashed by the Ryan pick, Romney led Obama in the Gallup tracking poll by 46 to 45 percent. Four days later, he was up by only 47 to 45 percent.

Following Biden's gaffe, former Republican presidential nominee John McCain, whose 2008 running mate Sarah Palin was highly criticized, suggested it might be "wise" to swap Biden for Secretary of State Hillary Clinton.

Carney shot back that while he has "great admiration" and respect for McCain, "one place I would not go for advice on vice presidential running mates is to Senator McCain."