"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.
"So, I'm looking forward to have Harry reveal his sources, and we will probably find out it's the White House."
Romney's campaign earlier rejected the majority leader's statement as "shameful."
Reid also raised eyebrows for invoking Romney's late father, himself a one-time presidential candidate.
"His poor father must be so embarrassed about his son," Reid told the Huffington Post.
George Romney, a Michigan governor, released 12 years of tax returns during his unsuccessful bid for the Republican presidential nomination in 1968. His son has released only his 2010 tax return and an estimate for 2011, years when he was preparing for his own presidential bid or already running.
Reid doubled down on the claim late Thursday, firing back at Romney in a written statement.