WASHINGTON -- President Barack Obama's campaign Friday put new pressure on Mitt Romney to release more tax returns, urging the Republican to release five years of data--and in return, the Democrats will go easier on him.

The Romney campaign resisted the offer.

Romney said Thursday that over the past 10 years, he’d never paid less than a 13 percent rate in income taxes, but refused again to release more of his returns. Friday, Obama campaign manager Jim Messina wrote Romney campaign manager Matt Rhoades with his new request.

"Governor Romney apparently fears that the more he offers, the more our campaign will demand that he provide," Messina wrote. "So I am prepared to provide assurances on just that point: if the Governor will release five years of returns, I commit in turn that we will not criticize him for not releasing more--neither in ads nor in other public communications or commentary for the rest of the campaign."

He sought five years of returns, from 2007 to 2012. Romney, governor of Massachusetts from 2003 to 2007, has released 2010 returns and estimates of his 2011 taxes. In 2010, he paid taxes at a 13.9 percent rate, and in 2011, he expected to pay at a 15.4 percent rate.

"In the Governor's case, a five-year release would appropriately span all the years that he has been a candidate for president," Messina said. "It would also help answer outstanding questions raised by the one return he has released to date, such as the range in the effective rates paid, the foreign accounts maintained, the foreign investments made and the types of tax shelters used."

He added: "The Governor and his campaign can expect in return that we will refrain from questioning whether he has released enough or pressing for more.”

Rhoades quickly doused much hope of a further release.

"It is clear that President Obama wants nothing more than to talk about Governor Romney’s tax returns instead of the issues that matter to voters, like putting Americans back to work, fixing the economy and reining in spending," he said in a note to Messina.

"If Governor Romney’s tax returns are the core message of your campaign, there will be ample time for President Obama to discuss them over the next 81 days.

"In the meantime, Governor Romney will continue to lay out his plans for a stronger middle class, to save Medicare, to put work back into welfare, and help the 23 million Americans struggling to find work in the Obama economy."

Soon to be nominated as the Republican presidential standard-bearer, Romney said Thursday he’d gone back and looked at his taxes, and found that "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."

At a news conference Thursday in Greer, S.C., Romney tried to defuse the political controversy over his stance, saying the commotion was "small-minded."

And he took aim at Senate Majority Leader Harry Reid, D-Nev., who charged earlier this month on the Senate floor that Romney had paid no taxes for a decade, but offered no proof. Reid said he’d heard that from a Bain Capital investor whom he refused to identify. Romney co-founded Bain, a private equity firm.

"I paid taxes every single year," Romney said. "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."