He said he was not aware the microphone was still on.
"It was not a public speech or a declaration," Jackson said, while noting that the comments "will not be helpful".
"For any harm or hurt that this hot mic private conversation may have caused, I apologise," he said in a written apology released earlier in the day.
"My support for Senator Obama's campaign is wide, deep and unequivocal."
Jackson said he had called Obama's campaign to apologise.
"It represents too much of dreams of so many who have paid such great prices, and I'm very sensitive to what that means," he said.
Jackson said the "hurtful and wrong" comments came in response to a question from a fellow guest during a break from taping Fox TV's Fox & Friends programme on Sunday.
The guest asked about speeches on morality that Obama has given at black churches.
Jackson declined to repeat the comments, but said he decided to apologise publicly after hearing from Fox News that it would air them.
In an interview to The Associated Press earlier Wednesday, Jackson said he did not remember his exact words, but said he was "very sorry".
The Fox News programme, The O'Reilly Factor, aired Jackson's comment on Wednesday night, including a slang reference to his wanting to cut off Obama's testicles.
The report bleeped out the slang but made clear what Jackson said with subtitles.
Meanwhile, Obama stoked speculation about Hillary Clinton being chosen as his running mate with an unannounced stop at the Washington law firm of a member of his vice-presidential search team. And then flying to New York fund raisers with Clinton and another search team member.
Aides were silent about why Obama and Clinton, along with Caroline Kennedy, a member of Obama's vice-presidential vetting team, travelled together on Wednesday other than to cite the fund raisers.
Kennedy introduced Obama at the first; Clinton, who represents New York in the senate, introduced him at the second.