Mitt Romney told Fox News he was committed to “helping the 100%”.
His comments, secretly filmed at a fundraiser in September, were possibly his most damaging campaign moment.
Polls suggest he is back on track after a debate with President Barack Obama this week. Barack Obama has urged him to reveal the true cost of his policies.
Observers say the president is seeking to portray his rival as dishonest about how middle class families will be taxed, while Mitt Romney wants to distance himself from his earlier gaffe.
After the video emerged from the private donors dinner in September, Mitt Romney said his remarks were “inelegantly stated” but did not retract them.
However, Mitt Romey went further in his interview with Fox on Thursday.
“Clearly in a campaign with hundreds if not thousands of speeches and question-and-answer sessions, now and then you are going to say something that doesn’t come out right,” he said.
“In this case I said something that’s just completely wrong. I absolutely believe, however, that my life has shown that I care about 100%… When I become president, it will be about helping the 100%.”
Most observers agree that Mitt Romney won the televised debate on Wednesday. A Reuters/Ipsos poll on Thursday suggested Mitt Romney had a net positive rating for the first time in the presidential campaign.
The poll said 51% of voters viewed him positively, with Barack Obama at 56%. The Republican moved ahead of his Democrat rival on which candidate voters trust to handle the economy, create jobs and manage the deficit.
Many of Barack Obama’s supporters are puzzled he chose not to bring up the 47% comments in the debate, although his campaign has used the remarks in a television advert.
At a rally in Denver on Thursday, Barack Obama urged his rival to tell the “truth” about his own policies.
“The real Mitt Romney has been running around the country for the last year promising $5 trillion in tax cuts that favor the wealthy. The fellow on stage last night said he didn’t know anything about that,” he said.
At a campaign rally in Virginia, Mitt Romney did not respond directly to the president’s criticism.
But he did argue that Barack Obama had failed during the debate to make his case for another term.
During Wednesday night’s head-to-head Mitt Romney repeatedly denied the $5 trillion claim.
Fact-checkers have said that Mitt Romney’s proposal to lower taxes by 20%, abolish estate tax and the alternative minimum tax would reduce revenue by $5tn over a decade.
The Republican has said he would help offset that by eliminating tax loopholes; the non-partisan Tax Policy Center says the sums do not add up.
The candidates went head to head for 90 minutes on jobs, taxes and healthcare.
Opinion polls agreed that Mitt Romney had the upper hand in the debate – the first of three between the White House rivals.
Various surveys gave Mitt Romney a 46-67% margin, with Barack Obama trailing on 22-25%.
The president was criticized for appearing hesitant and subdued, while the former governor – who has been lagging in the race – seemed animated and assertive.
Vice-presidential candidates Joe Biden and Paul Ryan will meet in Danville, Kentucky on 11 October, before the second presidential debate on 16 October.
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