LAS VEGAS (Reuters) - Under pressure to reveal more about his personal finances, Republican presidential candidate Mitt Romney on Friday said he had paid "a lot of taxes" every year.

Senate Majority Leader Harry Reid accused Romney on the Senate floor on Thursday of not paying taxes for 10 years, the strongest accusation yet by Democrats in a fight over the former private equity executive's tax records.

Romney strongly denied Reid's claim.

"Let me also say categorically: I have paid taxes every year. A lot of taxes. A lot of taxes," he said during a campaign stop in Las Vegas, in Reid's home state.

Romney said the sources of Reid's accusations may be within the White House or President Barack Obama's re-election campaign, which has frequently called on Romney to release more than the two years' worth of tax information that he has made public.

"By the way, Harry, I understand what you're trying to do here," Romney said. He accused the Reid of trying to deflect attention from discredited policies, and from the Senate's failure to pass a budget in three years.

Romney did not say which types of taxes he had paid, although financial information he released in January showed he had paid an effective tax rate of 13.9 percent in 2010 mostly from capital gains on investments. That is far below the 35 percent top tax rate for wages.

On Thursday, Romney told Reid "to put up or shut up."

The former Massachusetts governor's denial comes as he looks to move on from a shaky trip abroad last week and return to talking about Obama's record on the economy.

Romney faced questions on Friday about the tax plan he would attempt to implement should he win election in November. He said that he had no intentions of increasing Americans' tax burden.

"My plan is very clear," he said. "I will not raise taxes on the American people."

Romney also refuted the notion that the richest taxpayers would benefit disproportionately from his plan.

"Higher income people are not going to pay a smaller share if I'm president," he said.

Romney's appearance in Nevada comes the day after campaigning in Colorado, where he tried to regain his footing after a trip to Britain, Israel and Poland that was seen as unsuccessful.

(Reporting by Sam Youngman; Writing by Gabriel Debenedetti; Editing by Alistair Bell and Vicki Allen)