John Schnatter, who has been the public face of the global restaurant chain, caused controversy in May when he said: "Colonel Sanders called blacks n******.
He then complained that Mr Sanders, who founded KFC, had never received a backlash for using the racial slur.
According to Forbes, the 56-year-old also spoke about his early life in Indiana on the conference call, and claimed people used to drag African-Americans from trucks until they died.
Although Mr Schnatter's comments were apparently intended to illustrate his opposition to racism, several people on the call said they found his remarks offensive.
Mr Schnatter, who founded Papa John's in 1984 and owns 29% of the company, said: "News reports attributing the use of inappropriate and hurtful language to me during a media training session regarding race are true.
"Regardless of the context, I apologise. Simply stated, racism has no place in our society."
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Late on Wednesday, Papa John's confirmed it had accepted his resignation - adding that it plans to appoint a new chairman in the coming weeks.
He was forced to resign as Papa John's chief executive last year after he criticised the NFL for its handling of national anthem protests by players.