"I shouldn't have been such a wise guy," Mr Biden said on a subsequent call with the US Black Chambers, an African-American business group.
Mr Biden responded, "I do that to white media and black media because my wife has to go on at 6 o'clock."
Before the apology, the Trump campaign organised a conference call with reporters where US senator Tim Scott, who is black, said Mr Biden's comments were "arrogant and demeaning" and "negative race-baiting rhetoric".
Mr Wigdor said he and others at his firm still believed Ms Reade's allegation against Mr Biden, that he digitally penetrated her and groped her in the basement of a Capitol Hill office building when she worked as a low-level staffer in his Senate office in the spring of 1993.
In his statement, Mr Wigdor said his firm believed that Ms Reade had been "subjected to a double standard" in the media and that much of the coverage surrounding her biography had little to do with her claims against Mr Biden.
