Speaking on Friday while on the stump in Nevada, Romney addressed the claims head-on, stating: "I have paid taxes every year, and a lot of taxes. So Harry is wrong."
It comes a day after Reid turned up the heat over demands that the Republican candidate publish more of his annual returns to the IRS – an issue which has dogged Romney for weeks.
Speaking on the floor of the Senate, Reid said: "The word's out that he hasn't paid any taxes for 10 years. Let him prove he has paid taxes because he hasn't."
So far Romney has refused to release any more tax records other than the two years worth he made public back in January.
Those documents revealed that the former Massachusetts governor and his wife recorded an income of $21.6m dollars in 2010. Of that, they handed over $3m in tax at a rate just shy of 14%.
The couple's effective tax rate is expected to increase a little on 2011's earnings, when they are expected to pay 15.4% on $20.9m. On both years the rate of tax paid is far lower than the average American.
The presidential candidate has refused to release any further records, despite persistent demands from media and political allies of Barack Obama.
It comes amid speculation that the Republican candidate paid little or no tax in some years, and that he had squirrelled away vast chunks of his fortune in tax havens such as the Cayman Islands and Switzerland.
The latest accusation by Reid prompted a forthright response from Romney during a radio interview on Thursday evening. He carried on the fight Friday with statements while on the road.
The Republican candidate told reporters that the claims were "patently, simply false" and challenged his accuser to come clean over who had given him the information.
For his part, Reid has said his allegations came from an "extremely credible" source. Keeping the spat alive on Friday, the Senate leader accused Romney of insulting voters over his refusal to release any more tax returns. He also took a swipe at proposals that would see tax relief for the rich extended under a Republican presidency.
Describing the former Massachusetts governor as "the most secretive presidential candidate since Richard Nixon", Reid said: "It's hard to say which is more insulting to Americans' intelligence, Mitt Romney's tax plan or his refusal to show the American people what's in his tax returns."
Reid added: "Thumbing your nose at the people you're asking to vote for you won't fly in Nevada, just like it won't fly in the rest of the country."
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image: © Gage Skidmore