Jackson said at a news conference that he had replied that Obama's speeches can come off as speaking down to black people and that there were other important issues to be addressed in the community, such as unemployment, the mortgage crisis and the number of blacks in prison.
He said he was not aware the microphone was still on.
Jackson declined to repeat the comments, but said he decided to apologize publicly after hearing from Fox that it would air them.
In an interview with The Associated Press earlier Wednesday, Jackson said he didn't remember his exact words, but said he was "very sorry." He told CNN the remark was "regretfully crude."
Fox News aired Jackson's comment 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.
"It was not a public speech or a declaration," Jackson said at the news conference, adding the comments "will not be helpful."
"For any harm or hurt that this hot mic private conversation may have caused, I apologize," 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 called Obama's campaign to apologize.
Obama campaign spokesman Bill Burton noted that the Illinois senator grew up without his father and has spoken and written at length about the issues of parental responsibility and fathers participating in their children's lives, and of society's obligation to provide "jobs, justice and opportunity for all.
"He will continue to speak out about our responsibilities to ourselves and each other, and he of course accepts Reverend Jackson's apology," Burton said.
Jackson's comments sparked something of a family feud. His son, Rep. Jesse Jackson Jr., said he was disappointed by his father's "reckless statements."
"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," the younger Jackson said.
The comments are not the first the elder 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 wrong to use the term, but said he did so in private to a reporter.
