"Thanks for the note" -- but no thanks.

That was the response Friday from the Romney team after Obama's campaign manager tried once again to wrench more tax documents from the Republican president candidate, this time by offering to refrain from criticizing Mitt Romney's transparency if he agrees to release five more years of returns.

Romney campaign manager Matt Rhoades wrote a brief email to Obama campaign manager Jim Messina dismissing the offer.

"Thanks for the note. 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 wrote. "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."

The Obama campaign offer came after Romney said a day earlier that he's "never paid less than 13 percent" in taxes over the last 10 years.

Messina, pressing Romney once again for documentation, wrote that he wanted to offer "assurances" to allay Romney's concerns that releasing additional tax returns would just feed the Democrats' appetite for more.

"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," Messina wrote.

Messina, notably, did not offer to refrain from criticizing the contents of whatever documents Romney might furnish.

And that's the kind of criticism Romney has expressed concern about. Speaking on NBC's "Rock Center," wife Ann Romney voiced the same reservations. She said, before Messina's letter was sent out, that releasing more returns would give Democrats more ammunition, and claimed the campaign would not be releasing more.

Mitt Romney tried to clear the air on Thursday over the issue, offering his most expansive answer yet on the topic while speaking to reporters outside a South Carolina airport.

"I did go back and look at my taxes," Romney said. "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."

Democrats -- most notably Senate Majority Leader Harry Reid -- have hounded him for months over the issue. Reid went so far as to claim on the Senate floor, without offering proof beyond an unnamed source, that Romney hadn't paid taxes for 10 years, and then challenged Romney to prove him wrong.

Romney says the claim is "totally false." But Reid and the Obama campaign dug in on their position that it's Romney's obligation to prove he paid those taxes -- rather than their obligation to prove their charges are true.

Messina wrote in his letter that Romney would "only" have to release three more sets of returns -- on top of the 2010 and 2011 returns.

"This request for the release of five years, covering the complete returns for 2007-2012, is surely not unreasonable. Other Presidential candidates have released more, including the Governor's father who provided 12 years of returns," he wrote, adding that the campaign is looking for answers on "the range in the effective rates paid, the foreign accounts maintained, the foreign investments made, and the types of tax shelters used."

He closed: "And, I repeat, the Governor and his campaign can expect in return that we will refrain from questioning whether he has released enough or pressing for more."