SALT LAKE CITY – Mitt Romney, already struggling to stabilize his turbulent presidential campaign, confronted a mounting challenge Tuesday as a new video of controversial remarks to wealthy donors showed the Republican nominee saying that Palestinians have “no interest whatsoever” in reaching a peace agreement with Israel.

Romney told a private audience of campaign donors in May that the pursuit of peace in the Middle East is likely to remain “an unsolved problem” and that “the pathway to peace is almost unthinkable to accomplish,” according to the video released early Tuesday by Mother Jones magazine.

The clip is only the latest from Romney’s $50,000-a-plate fundraiser on May 17 in Boca Raton, Fla., now buffeting his campaign 49 days from Election Day.

On Monday, Mother Jones released grainy videos in which Romney dismisses President Obama’s supporters as “victims” who take no responsibility for their livelihoods and who think they are entitled to government handouts. He said that his job “is not to worry about those people. I’ll never convince them that they should take personal responsibility and care for their lives.”

On Tuesday afternoon, Mother Jones released the full video.

Romney and his campaign urgently tried to defuse the controversy Monday night, hastily arranging a news conference in Costa Mesa, Calif. The nominee stood by the remarks, although he conceded that they were “not elegantly stated” and that he had been “speaking off the cuff in response to a question.”

Aboard the campaign plane to Salt Lake City, adviser Kevin Madden said Romney was “very focused and determined” to shift the campaign focus to his core economic message.

“I still think this is an election that is focused on the economy, that’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 told reporters.

Asked whether Romney was “winning” at this stage, Madden said only that “it’s a very close, hard-fought campaign, and I think it will be all the day to Election Day.”

Romney is holding no public campaign events on Tuesday, but he could address his comments about the Israelis and Palestinians at his fundraisers in Salt Lake City and Dallas, which will be open to reporters. And aides added to his campaign schedule an interview on Fox News Channel, where he again talked about the “47 percent” remark.

“We were, of course, talking about a campaign and how he’s going to get close to half the vote, I’m going to get half the vote, approximately, I hope. I want to get 50.1 percent or more,” Romney said on “Your World with Neil Cavuto.”

“Frankly, we have two very different views of America. The president’s view is one of a larger government.... I believe the right course for America is one where government steps in to help those that are in need — we’re a compassionate people — but then we let people build their own lives, create enterprises.”

Although Romney has spoken skeptically in the past about the prospect for a so-called two-state solution, he has not used the kind of language on the campaign trail that he used in the closed-door fundraiser.

Romney’s hard-line approach at the fundraiser to the Israel-Palestinian conflict is in sync with the view of Israeli Prime Minister Benjamin Netanyahu, who has endorsed a two-state solution but with so many caveats that Palestinians say it is not viable. Like Romney, Netanyahu has also questioned the Palestinian leadership’s commitment to reaching a peace agreement.

Romney’s aides defended the candidate’s foreign policy remarks by arguing that there is “no news” in Romney’s comments. They said they are consistent with the policy views Romney already has laid out regarding a two-state solution.

“As he’s often said, there is this one obvious truth: peace will not be possible if the extreme elements of the Palestinian side refuse to come to the table for talks or to recognize Israel’s right to exist,” Romney spokeswoman Andrea Saul said.

Saul added, “A possible unity government between Hamas — a terrorist organization — in Gaza and Fatah in the West Bank would squelch the prospect for peace. Gov. Romney believes that the path to a two-state solution is to ensure the security of Israel and not to throw up any more barriers to the two sides engaging in direct negotiations.”

Romney is also trying to move past the furor sparked by his comments about the “47 percent” of Americans who he said are dependent on government entitlements by stressing that the remarks underscored the contrast between his and Obama’s different visions for the nation.

“This is ultimately a question about the direction for the country,” Romney told reporters Monday night. “Do you believe in a government-centered society that provides more and more benefits, or do you believe instead in a free-enterprise society where people are able to pursue their dreams?”

Romney’s running mate, Rep. Paul Ryan (Wis.), trumpeted the same theme of limiting government dependence at a town hall meeting in Dover, N.H.

“We shouldn’t be looking at people as if they’re stuck in some station or stuck in some class or some victim or something like that,” Ryan said. “We should look at every single human being in this country as people who are on their way toward opportunity. If they’re not doing well right now, what is it we need to do to help them get back on their feet so they can go make the most of their lives?”

Obama’s campaign quickly pounced, releasing a video Tuesday morning asking voters on the streets what they think of Romney’s remarks to his wealthy donors. And at the White House, press secretary Jay Carney said Romney’s comments were dividing the nation.

“When you are president of the United States, you are president of all the people, not just the people who vote for you,” Carney told reporters Tuesday. “Setting aside what Governor Romney thinks, the president certainly does not think men and women on Social Security are irresponsible or ‘victims,’ that students aren’t responsible or ‘victims.’”

Carney added that Obama believes the nation needs “to come together as a country and work for what’s best for the country, especially the middle class, which is the backbone of this nation.”

This comes at a troubling moment for the Romney campaign, as top donors and some advisers are going public with grievances about what they see as strategic blunders that have kept the Republican ticket from capitalizing on Obama’s lukewarm approval ratings and the poor state of the nation’s economy.

A spate of polls nationally as well as in critical battleground states show Obama gaining on Romney. In Virginia, for instance, a Washington Post poll released Tuesday has Obama with a clear lead over Romney, 52 to 44 percent.

Connecticut Senate candidate Linda McMahon, one of the GOP’s best hopes to pick up a seat, distanced herself from Romney’s comments in a statement posted to her campaign Web site early Tuesday.

“I know that the vast majority of those who rely on government are not in that situation because they want to be,” McMahon said. “People today are struggling because the government has failed to keep America competitive.”

Romney this week is attempting to reboot his campaign message, with advisers saying he would discuss more specific details of his five-step economic plan. For months, senior Republicans have urged Romney to be more specific in his campaign message, saying it is critical for him not just to attack Obama’s economic record but also to spell out concrete steps he would take as president to help middle-class families.

On Monday, Romney began a fresh offensive on the debt, and on Tuesday his campaign released two related television advertisements. The first, “Dear Daughter,” argues that Obama’s policies are making it harder on women, noting that every woman’s individual share of the national debt is over $50,000. The second, “Prairie Fire,” talks about the debt as a prairie fire sweeping across the nation’s heartland and threatening people’s homes and children.

But the campaign’s effort seemed to be overshadowed by Romney’s comments at the May fundraiser, with some Republicans voicing alarm about the state of the campaign.

Rick Davis, a top adviser to Sen. John McCain’s unsuccessful 2008 presidential bid, said Romney’s response in the coming days is “critical.”

“This is a character-building moment,” Davis said on “CBS This Morning.” “The American public looks in at various times during a campaign and I promise you they’ll be looking in this week.”

O’Keefe reported from Washington. Scott Wilson in Washington and Felicia Sonmez in Dover, N.H., contributed to this report.