Floyd Mayweather Jr has directed a homophobic slur at Conor McGregor after accusing him of making racist comments during the media tour to promote their Las Vegas fight.

The former five-weight boxing world champion will face the UFC lightweight title-holder in 12 rounds under boxing rules on August 26, and the two have been conducting a number of promotion press conferences over the past week.

McGregor attracted criticism for a series of comments during those events and is alleged to have made racist comments during the third stop of the tour in New York on Thursday.

"He called black people 'monkeys'," Mayweather said during a news conference at Wembley Arena on Friday. "He totally disrespected black women. Then he spoke disrespectfully to my mother and he spoke disrespectfully to my daughter."

Then, once the pair entered a boxing ring at the event for the official promotion, Mayweather told McGregor: "You punk. You faggot. You ho."

Mayweather retired undefeated in 2015 after winning all 49 of his bouts.