“I whispered in his ear that I wished he would just apologize and get it over with,” Ms. Cobb-Hunter recalled, noting that although Mr. Biden displayed little reaction, she did not think he appreciated the advice.

“The longer it drags on the more of a challenge it becomes, which is why I suggested he simply apologize and move on,” she said, adding that Mr. Biden was generally warmly received by what was a friendly group and that she did not hear anybody else raise the issue during the half-hour she was at the private meeting.

Mr. Biden’s longtime allies here voiced doubts that his comments would leave a lasting mark, but agreed that they were not helpful — particularly with younger voters who never knew official segregation.

“If I was in the campaign I’d probably be pulling my hair out this week, but I don’t think they’ll do any lasting damage,” said the Rev. Joseph A. Darby, a pastor and supporter of Mr. Biden.

In brief remarks before a fish fry crowd sweltering in the evening heat, Mr. Biden made no mention about the controversy and won applause for saying it’s important Democrats rally behind whoever the nominee is next year.

Taking back the microphone, Mr. Clyburn joked: “That’s the shortest speech Joe Biden ever made.”

Each of the candidates here — Gov. Steve Bullock of Montana and Mayor Pete Buttigieg of South Bend, Ind., were the only two not in attendance Friday — were planning to address delegates at the convention on Saturday, which is also being broadcast on MSNBC.

In addition to the convention, most of the candidates were also planning to address a nearby forum on Saturday that’s being sponsored by Planned Parenthood which is expected to draw a few hundred, mostly female activists. In the 2016 Democratic presidential primary here, over 60 percent of voters were women.

Although South Carolina has not passed a virtual ban on abortion the way Alabama and Georgia have, abortion-rights activists are deeply concerned that a measure banning the procedure after a fetal heartbeat has been detected, which passed in the state House this year, could become law next year.