A day after the hastily arranged press conference in which Mitt Romney admitted that his controversial comments about President Barack Obama's supporters—unearthed in a video secretly taped at a fundraiser—were "not elegantly stated," the Republican presidential nominee sat down with Fox News' Neil Cavuto for his first interview since the dustup.

Just as he did Monday, Romney stood by his remarks.

"Frankly, we have two very different views about America," Romney said of the president. Obama's view "is of a larger government" and "a pathway that looks more European than American, in my view.

"I disagree," he said.

[Related: Amid campaign turmoil, Romney tries to stay 'focused']

Romney referenced a 1998 audio recording—leaked online Tuesday—in which Obama said he believes in the redistribution of wealth in America.

"The government steps in to help people in need—we're a compassionate people—but then we let people build their own lives, create enterprises," Romney told Cavuto. "We believe in free people and free enterprise—not redistribution."

In the clip from the surreptitiously recorded tape released Monday by Mother Jones, a left-leaning magazine, Romney told a group of donors in Boca Raton, Fla., in May that he believes people who plan on voting for Obama "no matter what"—a group Romney categorizes as about 47 percent of all voters—are "victims" who do not pay income tax and are reliant on government handouts.

[Also read: Romney stands by comments but says they were 'not elegantly stated']

"I believe that we should have enough jobs and enough take-home pay such that people have the privilege of higher incomes that allow them to be paying taxes," Romney said on Tuesday. "I think people would like to be paying taxes."

At the Monday night news conference, Romney said his fundraising comments were "off the cuff" and called for the full video to be released to show them in context. (On Tuesday, Mother Jones released the full 50-minute video.) "I'm sure I can state it more clearly in a more effective way than I did in a setting like that and so I'm sure I'll point that out as time goes on."

But, he added, "it's a message which I am going to carry and continue to carry."

[Watch: The full secretly taped Romney fundraising video]

Partial clips from the event have been online for months, but escaped widespread notice. An anonymous leaker began promoting audio-only clips in comments on the Huffington Post's website, which caught the attention of Democratic researcher James Carter, former President Jimmy Carter's grandson. Carter alerted Mother Jones' David Corn, who competed with the Huffington Post to persuade the anonymous leaker to give him the full video. Finally, the leaker decided to give the full clips to Corn, who published them Monday.

Asked what he thought about the involvement of Carter's grandson, Romney said: "I hadn't heard that one, Neil. I'm not too concerned about the source."