COSTA MESA, Calif. (AP) — Republican Mitt Romney faced a new challenge Tuesday for saying Palestinians “have no interest” in peace with Israel, comments captured on newly released videotape of his private remarks to wealthy donors.

“You hope for some degree of stability, but you recognize that this is going to remain an unsolved problem … and we kick the ball down the field and hope that ultimately, somehow, something will happen and resolve it,” Romney said. He said pushing Israel to give up disputed territory for a two-state solution with the Palestinians “is the worst idea in the world.”

The clip is the second to surface this week of Romney’s remarks at a $50,000-a-plate fundraiser in Boca Raton, Fla., on May 17. Romney’s campaign spent part of Monday trying to mitigate fallout from the first clip, in which Romney tells donors that 47 percent of Americans “believe they are victims” entitled to help from the government that permeates their lives.

At an impromptu news conference Monday night, Romney offered no apologies, conceding the comments were not “elegantly stated” and were spoken “off the cuff.” The Republican presidential nominee said the remarks showed a contrast between President Barack Obama’s “government-centered society” and his belief in a “free-market approach.”

“Of course, I want to help all Americans, all Americans, have a bright and prosperous future,” Romney told reporters.

Obama’s campaign pounced on the first video, which was obtained by the magazine Mother Jones and released only hours after Romney’s campaign outlined a new strategy to try to rejuvenate a struggling campaign. The video’s emergence came as advisers to the former Massachusetts governor tried to reassure party leaders and donors about Romney’s strategy amid concerns that the race could be slipping away.

Romney has not addressed his remarks about the Middle East. He had no public appearances scheduled Tuesday.

His words put him in sync with hard liners in the Israeli government, including some aides to Israeli Prime Minister Benjamin Netanyahu and senior Israeli cabinet ministers. Netanyahu himself has publicly advocated for a two-state solution.

The Obama administration favors a two-state solution with Israel and a future Palestine. But it says Palestinian statehood can only come about through a negotiated agreement between the parties, not through the United Nations.

Palestinian lawmaker and scholar Hanan Ashrawi accused Romney of “destroying the chances for peace” and called his remarks “irresponsible and dangerous and both ignorant and prejudiced.”

Netanyahu’s office declined to comment. The office of Palestinian President Mahmoud Abbas also had no comment.

Romney’s comments in the first video appeared to focus more on the economy, the No. 1 issue for voters in November.

“There are 47 percent of the people who will vote for the president no matter what,” Romney is shown saying in the video of a May 17 fundraiser in Boca Raton, Fla. “There are 47 percent who are with him, who are dependent upon government, who believe that they are victims, who believe that government has a responsibility to care for them, who believe that they are entitled to health care, to food, to housing, to you name it.”

Romney said in the video that his role “is not to worry about those people. I’ll never convince them they should take personal responsibility and care for their lives.”

In a seven-minute news conference with reporters before a fundraiser near Los Angeles, Romney did not dispute the authenticity of the hidden-camera footage. He called for the release of the full video, instead of just the clips posted online. He sought to clarify his remarks but did not apologize when asked if he was concerned that he may have offended people.

“It’s not elegantly stated, let me put it that way. I was speaking off the cuff in response to a question. And I’m sure I could state it more clearly in a more effective way than I did in a setting like that,” Romney said.

About 46 percent of Americans owed no federal income tax in 2011, although many of them paid other forms of taxes. More than 16 million elderly Americans avoid federal income taxes solely because of tax breaks that apply only to seniors, according to the nonpartisan Tax Policy Center.

Real estate magnate Donald Trump, a Romney campaign surrogate, said he thought the former Massachusetts governor should not say he’s sorry for his remarks.

Interviewed on NBC’s “Today” show Tuesday, Trump said: “What he said is probably what he thinks. … He’s saying that that’s not what he really meant. I’m sure he wishes he hadn’t said it.”

But Trump said Romney “won’t get the votes of a lot of people he’s discussing. … Do not apologize.”

The videos were the latest troubles for Romney’s campaign, which has tried to focus attention on a weak economic recovery and make the case that the Republican’s business background would help spur the economy. In recent weeks, the campaign has dealt with the fallout from Clint Eastwood’s rambling conversation with a chair at the Republican convention and Romney’s omission of the war in Afghanistan or thanks to the troops in his prime-time convention speech.

The eruption of violence in Egypt and Libya last week prompted Romney to issue a statement assailing the Obama administration before it was known that an American ambassador and three other U.S. citizens had died in Libya, a move that generated criticism from Democrats and Republicans alike.

A series of polls have shown Obama with an edge nationally and in key battleground states, leading Republicans to implore Romney to give voters more specifics on how he would govern. The new approach aims to improve Romney’s standing in the lead-up to the first presidential debate on Oct. 3.

Obama campaign manager Jim Messina quickly issued a fundraising appeal based on the initial video, telling supporters: “If we don’t come through for President Obama right now, this will be the guy making big decisions that affect us and our families every single day.”

An Obama adviser said the Democratic campaign might use Romney’s comments from the fundraising video in television advertisements. The official wasn’t authorized to discuss campaign strategy publicly and requested anonymity.

Romney’s campaign released a separate television ad Tuesday, arguing that the president’s policies “are making it harder on women.” It cited unemployment and poverty statistics for women in an attempt to close the gender gap that has shown women favoring Obama.