The camera appears to be hidden on a marble-topped sideboard and shows Romney addressing more than half a dozen people who are sitting eating. Waiters, some wearing white gloves, serve the guests.
"I look at the Palestinians not wanting to see peace anyway, for political purposes, committed to the destruction and elimination of Israel, and these thorny issues, and I say there's just no way," Romney said.
William Kristol, editor of the conservative Weekly Standard, called Romney's comments "stupid and arrogant."
David Brooks, a self-described "moderate conservative" columnist in The New York Times, said Romney did not appear to understand American culture.
Two Republican candidates for the US Senate in Democratic-leaning states, Linda McMahon in Connecticut and Senator Scott Brown in Massachusetts, distanced themselves from Romney's comments.
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McMahon said she disagreed with Romney and "the vast majority of those who rely on government are not in that situation because they want to be."
Brown said in an email to The Hill newspaper that Romney's views did not reflect "the way I view the world."
The video capped a difficult two weeks for Romney, who has fallen slightly behind Obama in opinion polls, taken heavy criticism for a hasty attack on the President during assaults on US diplomatic compounds in Egypt and Libya and faced damaging news reports about infighting in his campaign team. Romney video: fatal gaffe, or bump in the road?
It also reinforced criticism that the millionaire former head of the private equity firm Bain Capital is out of touch with average Americans, a theme the Obama campaign has hammered home all summer through advertisements.
Romney did not back away from the remarks at a Monday night news conference in California, where he said they were "not elegantly stated," or again on Tuesday in an interview with Fox News.
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Romney cited a 1998 video of Obama discussing his belief in wealth distribution "at a certain level to make sure everybody's got a shot." Romney said he and Obama had very different views of America.
"I think a society based upon a government-centered nation where government plays a larger and larger role, redistributes money - that's the wrong course for America," Romney said on Fox.
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In the video, Romney also said in response to an audience question that he would try to take political advantage of a foreign crisis similar to the Iran hostage episode that damaged President Jimmy Carter in 1980.
"I mean, if something of that nature presents itself, I will work to find a way to take advantage of the opportunity," he said.
Democrats leaped at the chance to criticize Romney for the comments and launched a new ad and fund-raising campaign focused on them. On the West Bank, Palestinians said Romney was wrong to accuse them of not seeking peace.
VIDEO "No one stands to gain more from peace with Israel than Palestinians and no one stands to lose more in the absence of peace than Palestinians," chief Palestinian negotiator Saeb Erekat told Reuters.
"Only those who want to maintain the Israeli occupation will claim the Palestinians are not interested in peace."
The video controversy overshadowed an effort by Romney's campaign to offer more economic policy specifics and air new television ads to address rising worries from Republicans about the direction of his campaign.
'Still focused on economy'But Romney adviser Kevin Madden said the firestorm over the video would not distract from the campaign's economic focus.
"I still think this is an election that's focused on the economy, it's focused on the direction of the country, and I think the voters right now who have yet to make up their mind are still viewing it through the lens of that," Madden said.
A short version of the video was spotted on YouTube in August by
, the grandson of the former Democratic president. James Carter IV
The self-styled opposition researcher tracked down and convinced the person who recorded the video to hand over the full version to David Corn, a journalist with Mother Jones.
"James, this is extraordinary. Congratulations! Papa," Jimmy Carter told his grandson in an email on Tuesday, according to NBC News.
Some Republicans rallied to Romney's defense. Former White House Chief of Staff John Sununu, a Romney adviser, said the Obama campaign was trying to wage class warfare.
Donald Trump urged Romney not to apologize and told NBC's Today show that "Republicans have to get tougher or they are going to lose this campaign."
The video comes seven weeks before the election and just more than two weeks before the first presidential debate on October 3, which may be Romney's best chance to change the direction of the White House race.
US Republican presidential nominee Mitt Romney speaks at campaign fundraiser in Dallas, Texas. Reuters
Romney regained some ground on Obama in a on Tuesday, trailing by 4 percentage points, 47% to 43%. Reuters/Ipsos online poll
Romney had trailed by 5 points on Monday. The national Real Clear Politics average of polls gave Obama a 2.9-point lead over Romney.
Romney's comments about the 47% of Americans who do not pay taxes and are dependent on government were not a new theme for Republicans, and it was a largely accurate figure.
About 46% of US households paid no federal income tax in 2011, according to the bipartisan Tax Policy Center, although almost two-thirds of those paid an employment tax to support the Social Security and Medicare programs.
In most cases, it is elderly and poor households that do not pay federal income tax, the center said. About half of those who pay no tax are allowed to do so because their incomes are too low.
VIDEO What did Romney say: Palestinians not interested in peace: Romney video Secret video shows Romney rubbishing half the country After Romney gaffe, Obama's reactions: Obama job approval rising, race still tight: poll Obama jabs at Romney over his '47%' remarks President of all Americans, but happy to have rich friends What now? Romney video: fatal gaffe, or bump in the road? Despite his rhetoric, Romney needs the '47%' to win Will Romney's troubles rub off on congressional races?