CHICAGO, Illinois (CNN) -- The Rev. Jesse Jackson apologized Wednesday for "crude and hurtful" remarks he made about Democratic presidential candidate Sen. Barack Obama after an interview with a Fox News correspondent.

The Rev. Jesse Jackson apologized to Sen. Obama's campaign Wednesday over "hurtful" remarks.

The remarks came Sunday as Jackson was talking to a fellow interviewee, UnitedHealth Group executive Dr. Reed V. Tuckson. An open microphone picked up Jackson whispering, "See, Barack's been talking down to black people ... I want to cut his nuts off."

Jackson told CNN's "Situation Room" that he didn't realize the microphone was on.

"It was very private," Jackson said, adding that if "any hurt or harm has been caused to his campaign, I apologize."

An Obama campaign spokesman, Bill Burton, said that the senator from Illinois "of course accepts Rev. Jackson's apology." Watch Jackson whisper comments about Obama »

Jackson's son, Rep. Jesse Jackson Jr. of Illinois -- co-chair of Obama's presidential campaign -- publicly blasted his father's comments Wednesday.

"I'm deeply outraged and disappointed in Rev. Jackson's reckless statements about Sen. Barack Obama," the younger Jackson said. "His divisive and demeaning comments about the presumptive Democratic nominee -- and I believe the next president of the United States -- contradict his inspiring and courageous career."

Jackson Jr. added that he'll "always love" his father. But, he said, "I thoroughly reject and repudiate his ugly rhetoric."

The elder Jackson repeated his apology in a news conference in Chicago a couple of hours before Fox News aired Sunday's remarks. He said he wanted to address the issue publicly before the cable network aired the comment, because "I know that they will further violate the context of it."

Earlier, Jackson told CNN he felt "very distressed because I'm supportive of this campaign and with the senator." Watch more of Jackson's apology on CNN »

"I was in a conversation with a fellow guest on Sunday. He asked about Barack's speeches lately at the black churches. I said he comes down as speaking down to black people," Jackson said.

In a recent Father's Day speech at a black church, Obama took absent black fathers to task, saying, "We need them to realize that what makes you a man is not the ability to have a child -- it's the courage to raise one."

While Jackson didn't cite any particular comment, he told CNN that Obama's message to black voters must be broader and serve as more than a "moral challenge."

The black community is faced with high levels of unemployment, home foreclosures and violence, "so we have some real serious issues -- not just moral issues," he said.

However, Jackson said after finding out about the open microphone, he immediately contacted the Obama campaign to apologize.

Burton, Obama's spokesman, said the senator is quite familiar with the issues facing African-Americans and that "he will continue to speak out about our responsibilities to ourselves."

"As someone who grew up without a father in the home, Sen. Obama has spoken and written for many years about the issue of parental responsibility, including the importance of fathers participating in their children's lives," Burton said. "He also discusses our responsibility as a society to provide jobs, justice, and opportunity for all."

The Rev. Al Sharpton, president of the civil rights group National Action Network, said Jackson's remarks were "most unfortunate," adding he was happy that Jackson apologized.

"I hope people will remember the great work he's done in this country as one assesses this last incident," Sharpton said in a statement.

Sharpton said people "must be careful not to segregate Sen. Obama and impose some litmus test that is unfair and unproductive."

"We must be very clear that Sen. Obama ... is running for president for all Americans, not just African-Americans -- which is why most Americans have embraced his campaign," Sharpton said.

At Wednesday evening's news conference in Chicago, Jackson said: "I have supported Barack's campaign with passion from the very beginning." Watch Jackson's comments in Chicago »

Jackson, whose Rainbow/PUSH Coalition is based in Chicago, has publicly endorsed Obama, most recently in a piece published Tuesday in the Chicago Sun-Times, and said he enjoys a close relationship with the Obama family.

The incident is the latest of several in which the issue of Obama's relationship with the African-American community has become a part of the campaign, raised either by opponents or by Obama's allies.

Nearly two weeks ago, Ralph Nader -- who is running his own presidential campaign as an independent -- accused Obama of attempting to "talk white" and appealing to "white guilt" in his quest for the White House.

"There's only one thing different about Barack Obama when it comes to being a Democratic presidential candidate. He's half African-American," Nader told Colorado's Rocky Mountain News in a June 26 story.

Obama is still bouncing back from the weeks-long controversy over his former minister, the Rev. Jeremiah Wright, whose fiery sermons at Chicago's Trinity United Church of Christ drew unwanted attention for the campaign. In the sermons, Wright suggested the U.S. government may be responsible for the spread of AIDS in the black community and equated some American wartime activities to terrorism.

Wright's sermons and his eccentric behavior at later public appearances became a major political headache for the Obama campaign, especially since Wright officiated the senator's wedding, baptized both of his children and was a spiritual adviser to his presidential campaign until he was asked to step down in March.

This week's remarks by Jackson were not the first time he criticized Obama. Last fall, he was critical of Obama's reaction to the severe charges filed against six black students in the beating of a white student in Jena, Louisiana, a racially charged case that sparked a national outcry.

Jackson accused Obama of "acting like he's white," according to a South Carolina newspaper that cited a speech by Jackson at the historically black Benedict College in Columbia.

"If I were a candidate, I'd be all over Jena," Jackson said, according to the The State newspaper. "Jena is a defining moment, just like Selma [Alabama] was a defining moment."

The newspaper reported Jackson later said he did not recall saying Obama is "acting like he's white," but he continued to criticize Obama and other presidential candidates for not bringing more attention to the issue.

During the Democratic primary race, Jackson also said Sen. John Edwards was the only candidate speaking to the issues of the black community. He later apologized.

CNN's Don Lemon contributed to this story.

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