Mitt Romney on Thursday pushed back against Senate Majority Leader Harry Reid's allegations that the presumptive GOP nominee has not been paying his taxes.

"It's time for Harry to put up or shut up," Romney said on Sean Hannity's radio show.

In a Huffington Post interview published Tuesday, the leading Democrat said that an unnamed investor with Bain Capital, Romney's former private equity firm, told Reid in a phone conversation that Romney had not paid taxes for a decade.

Reid stood by the allegations on Thursday while speaking on the Senate floor.

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

Democrats and President Barack Obama's re-election campaign have repeatedly called for Romney to release more tax documents to answer any questions about his financial portfolio.

Romney has made public the full 2010 tax return and an estimate for 2011, with a pledge to release the full year once it's complete. He filed an extension for an October deadline.

Critics have hit back against Reid's comments this week, faulting him for making claims based off an anonymous source.

"Harry's gonna have to describe who it is he spoke with because of course that's totally and completely wrong," Romney said Thursday in the radio interview. "It's untrue, dishonest and inaccurate. It's wrong. So I'm looking forward to have Harry reveal his sources and we'll probably find out that it's the White House."

Mirroring Romney's comments, senior campaign adviser Eric Fehrnstrom described Reid's comments as "shameful, pathetic, baseless and untrue" and argued the majority leader, with the help of the Obama campaign, was attempting to "engage in McCarthy-like accusations about Mitt Romney."

"Four years ago Barack Obama said he was going to come to Washington and change the politics. Instead the Obama campaign has turned into a bottomless pit. Every day they reach a new low," he said Thursday on CNN's "The Situation Room."

Adding on, Fehrnstrom said Romney has "never zeroed out his tax liability" and "has always paid 100% of what was owed."