Republican presidential candidate Mitt Romney fired back at Senate Majority Leader Harry Reid on Thursday, saying the Nevada Democrat needed to "put up or shut up" regarding his claim that Romney had failed to pay taxes for ten years.

Reid set off a firestorm by citing an anonymous investor from Bain Capital, the investment firm Romney used to head, who allegedly said that Romney had not paid taxes in a decade. Questions have swirled around Romney's taxes as the presumptive Republican nominee has refused to release more tax returns amid allegations he has stashed holdings in overseas accounts.

"The word's out that he hasn't paid any taxes for 10 years," Reid said in a Tuesday interview. "Let him prove that he has paid taxes, because he hasn't."

The Senate's top Democrat added that he was not sure the allegation was true, but it still bolstered the perception -- pushed by President Obama's re-election campaign -- that Romney has been less than honest about how his income is taxed.

Romney sought to rebut the claim on Thursday, hitting back at Reid during an interview with Fox News' Sean Hannity. 

"Harry's going to have to describe who it is he spoke with, because, of course, that is totally and completely wrong," Romney said. "It's untrue, dishonest and inaccurate. It's wrong."

Romney pushed Reid to reveal who his source was and suggested that it was likely the White House, essentially suggesting that the Obama administration had leaked the charge to try and damage Romney.

That parallels Romney's continuing assault on the Obama administration for a series of leaks that have led to press reports detailing a computer virus unleashed on Iran, the Central Intelligence Agency's role in foiling a bomb plot in Yemen, and the Obama administration's handling of drone strikes. Romney has suggested that the administration itself made the leaks for political gain, compromising national security in an effort to enhance the president's image.

Reid has stuck to his guns, saying in a statement released on Thursday that it was "clear Romney is hiding something" and saying Romney had an obligation to release tax returns that he has so far withheld.

"When it comes to answering the legitimate questions the American people have about whether he avoided paying his fair share in taxes or why he opened a Swiss bank account, Romney has shut up," Reid said. "But as a presidential candidate, it's his obligation to put up, and release several years' worth of tax returns just like nominees of both parties have done for decades."