Mayweather said it's racist that McGregor is praised for his smack talk while he is criticised by commentators and media personalities.
"I don't really know the McGregor guy - never seen him fight," Mayweather said.
"I heard his name actually from one of the runners that works for our company.
"He told me about the guy McGregor. They say he talk a lot of trash and people praise him for it, but when I did it, they say I'm cocky and arrogant. So biased! Like I said before, all I'm saying is this, I ain't racist at all, but I'm telling you racism still exists."
Now McGregor has responded.
In a post to his official Instagram account McGregor took aim at the 49-0 fighter, telling him to get back in line.
"Floyd Mayweather, don't ever bring race into my success again," McGregor said.
"I am an Irishman. My people have been oppressed our entire existence. And still very much are.
"I understand the feeling of prejudice. It is a feeling that is deep in my blood.
"In my family's long history of warfare there was a time where just having the name "McGregor' was punishable by death.
"Do not ever put me in a bracket like this again. If you want we can organise a fight no problem. I will give you a fair 80/20 split purse in my favour seen as your last fight bombed at every area of revenue.
"At 27 years of age I now hold the key to this game. The game answers to me now."
In the post, McGregor also responded to criticism he has received for being pictured with what appeared to be a weapon.
McGregor posted a photo of a person holding what is being reported as likely a replica or toy gun in a seemingly parked car on Instagram early Thursday morning, and he may be facing issues in Ireland as a result.
In the photo, two people are in the car, with one wearing a ski mask which covers most of the face and holding what looks like a black firearm out of the window towards the camera.
A UFC official told FOX Sports that the promotion is aware of the posted photos and that they have been in contact with Conor McGregor's manager, Audie Attar.
Ireland has some of the most stringent firearm laws in the world. Several European media outlets are reporting that it is believed what the person in the photo is holding is a replica or airsoft gun - McGregor was recently seen shooting such a gun in a video - but even that could create a problem for him.
McGregor said in his most recent Instagram post that he was simply conducting research for his future film career.
"I apologise for having the air-soft in public," he said.
"I was simply rehearsing for a potential upcoming film role.
"I understand that the more traffic a story can get the more revenue it generates. So I understand and respect that the media must create these stories and these situations even if at times it is at other people's expense.
"We've all got to eat. And I eat well.
"So I will not complain."
- news.com.au
