The Obama campaign has said if Republican presidential candidate Mitt Romney releases five years of tax returns, they will drop the issue.

Mr Romney, who has made public his 2010 taxes and plans to do the same with his 2011 returns, rejected the offer.

The former private equity chief said on Thursday he had never paid under 13% in taxes over the past 10 years, a much smaller rate than most US wage-earners.

Mr Romney will challenge President Barack Obama in November's election.

Obama campaign manager Jim Messina made the tax-returns offer to his counterpart, Matt Rhoades, in a letter on Friday.

'No more tax releases'

"Governor Romney apparently fears that the more he offers, the more our campaign will demand that he provide," Mr 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."

Releasing several years of tax returns has become a standard move in recent presidential elections.

Image caption President Obama has said he would raise taxes on the wealthiest Americans

And Mr Messina noted that the Republican candidate's father, former Michigan Governor George Romney, had released 12 years of his tax returns during his own unsuccessful run for the presidency in 1968.

Mr Rhoades rejected the offer in an email that began: "Hey Jim, 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.

"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 candidate's wife, Ann Romney, reiterated that they were "hiding nothing" in an interview with NBC News on Thursday.

"We have been very transparent to what's legally required of us," Mrs Romney said. "There's going to be no more tax releases given."

Mitt Romney career highlights 1984: Founds Bain Capital, a private equity firm

Founds Bain Capital, a private equity firm 1994: Unsuccessful Senate race against veteran Massachusetts Democrat Ted Kennedy

Unsuccessful Senate race against veteran Massachusetts Democrat Ted Kennedy 1999: Takes over running of Salt Lake City Winter Olympics

Takes over running of Salt Lake City Winter Olympics 2002: Becomes governor of Massachusetts

Becomes governor of Massachusetts 2008: Unsuccessful bid for Republican presidential nomination

Unsuccessful bid for Republican presidential nomination 2012: Due to be anointed as Republican presidential nominee Profile: Mitt Romney Do the super-rich pay their way?

She added that releasing more information would only give their Democratic opponents more "ammunition".

Mr Romney has said he is following the example of Republican Senator John McCain, who released two years of returns in 2008 when running against Mr Obama.

He has said his critics would only distort his tax information if he divulged more.

Democrats have repeatedly questioned whether the former Massachusetts governor has something to hide about his estimated net worth of about $250m (£159m).

Democratic Senate Majority Leader Harry Reid has accused Mr Romney of not paying taxes in some years - a claim denied by the Republican.

The top tax rate for wages in America is 35%, but taxes on capital gains are lower.

Some 44% of Americans believe that raising taxes on the wealthiest would help the economy, according to a Pew Research Center Poll last month. Just 22% said they believed the opposite.

The same poll suggested that Americans believed two to one that Mr Obama's tax proposals would make the tax system more fair.