Jackson says his comments were picked up by a microphone during what he thought was a private conversation.
Jackson talked with reporters about the apology Wednesday evening at Rainbow PUSH headquarters.
This is something of a pre-offensive strike on Reverend Jackson's part. He said his comments have not yet aired but admits that they were critical of Senator Obama and a recent speech that Senator Obama gave in Chicago on Father's Day.
"It has to do with a tragic history. But we can't keep on using that as an excuse," Obama said that day to applause. "Any fool can have a child. That doesn't make you a father."
Jackson's comments came on Fox News during an interview on healthcare. He said something which some have characterized as crude remark about the senator. But that was during a break. He says he was unaware that his microphone was still hot and that those remarks were being recorded. But he also says that he takes full responsibility and that he should have known better.
"If anything I've said on a hot mic, statement that's attributed as a distraction, I offer an apology for that because I don't want harm or hurt to come to this campaign," said Rev. Jackson.
His son, Congressman Jesse Jackson Jr. issued a scathing statement a little bit earlier Wednesday. He is a strong Obama supporter. He said that, "Reverend Jackson is my dad and I'll always love him."
But he goes on to say in that, "I thoroughly reject and repudiate his ugly rhetoric. He should keep hope alive and any personal attacks and insults to himself."
Reverend Jackson declined to respond to that statement but said he wants to get this all behind him and turn the attention back to Obama's platform.
Senator Obama's office issued a statement as well. Obama says that he has given remarks similar to those he made in the church Father's Day for many years. He said he grew up in a fatherless home and he believes very strongly in the responsibility that fathers must take and that he plans to continue speaking on that issue.
Regardless of that, however, Obama said he accepts Reverend Jackson's apology.
Jackson said he commented in response to a question from a Fox News reporter about speeches on morality that Obama has given at black churches. A Fox spokeswoman said the comments came during a conversation with a Fox & Friends guest before a live interview Sunday from Chicago.
The reverend said Wednesday that he had said Obama's speeches "can come off as speaking down to black people" and that there were other important issues to be addressed in the black community, such as unemployment, the mortgage crisis and the number of blacks in prison.
"And then I said something I thought regretfully crude but it was very private and very much a sound bite and a live mic," Jackson told CNN.
The remarks apparently include a reference to male genitalia.
Chicago Tribune columnist Clarence Page, who has been booked on the Fox program "The O'Reilly Factor" to respond to Jackson's comments, reported that Jackson recalled his remark as, "The senator is cutting off his you-know-what with black people."
Jackson told The Associated Press that he doesn't remember "exactly" what he said Sunday but that he was "very sorry."
Rev. Jackson said he has called Obama's campaign to apologize.
"My appeal was for the moral content of his message to not only deal with the personal and moral responsibility of black males, but to deal with the collective moral responsibility of government and the public policy...," Jackson's statement said of his comments.
"That was the context of my private conversation and it does not reflect any disparagement on my part ... or my pride in Senator Barack Obama," he said.
Though Rev. Jackson is supporting Obama, the two are not close.
And Rev. Jackson is the third Chicago pastor to create problems for Obama on the campaign trail.
In March, a videotape of Obama's longtime former pastor Rev. Jeremiah Wright Jr. created a political firestorm in the primaries. On the tape, Wright accused the U.S. government of creating AIDS and is seen shouting "God damn America" during a sermon at Trinity United Church of Christ in Chicago.
In May, Roman Catholic priest the Rev. Michael Pfleger mocked Obama's then Democratic rival Sen. Hillary Clinton during a guest sermon at Obama's former church, from which Obama has since resigned. Pfleger, who is white, pretended he was Clinton crying over "a black man stealing my show."
The comments about Obama are not the first Jackson has had to explain after believing he was off the record.
In 1984, he called New York City "Hymietown," referring to the city's large Jewish population. He later acknowledged it was the wrong to use the term, but said he did so in private to a reporter.
The Associated Press contributed to this report.