Mayweather refused to answer questions about his own exchange with McGregor, but the Irishman insisted it arose because, unlike the other fighters on the weekend's bill, they did not have a face-off and offense was taken when he asked why.
"There was a face-off [scheduled], then there was no face-off, and then I saw him and said, 'What, are you afraid of a face-off today?' McGregor explained.
"He didn't say anything, but then the goons, the big goons that he surrounds himself with started pushing and shoving.
"And then it was just a pushing and shoving contest, and that was it. Nothing really happened. I didn't hear what his response was. It just became a pushing and shoving match."
Mayweather wore a fedora and gold rimmed glasses while McGregor sported a three-piece suit and tie and aviator sunglasses as they made separate appearances before a crowd of several hundred people in front of the arena.
"The fight is not going the distance, no matter what he says. He's getting knocked out," said Mayweather, who also accused McGregor of being overweight.
Mayweather will not cancel the fight if McGregor misses weight, but the Irishman would have to pay Mayweather millions in a fine.
When told of the American's confidence of a KO, the Irish UFC fighter responded: "I believe I am going to knock him down in the first round because be sure I am going to start fast.
"After that, maybe I will toy with him for two or three rounds and it's possible the referee will have to step in and stop it. Come Saturday night [Sunday], the king of the UFC will be the king of boxing as well."
For the 40-year-old Mayweather, the fight, his 50th, is expected to be his last - whatever the outcome.
"I've promised my children and I've promised the people around me that this is the last one," he said.
"'You know that when you push your body to the limit and beaten everyone out there that now the time has come."
However, he has promised the fans that he wants to go out in style.
"I want this one to be a great event. The people deserve the excitement. And like [Manny] Pacquiao, when I hit him with a big right hand in the first couple of rounds and the strength went out of him, this man is going to find out that the place he's in and the power are something completely different."
Who said it: McGregor v Mayweather edition
The fight could be seen by a staggering 50 million people in the United States alone and threatens the pay-per-view revenue record set by Mayweather and Pacquiao two years ago.
"It's a cultural event that crosses all demographics and all social and economic factors," said Mark Taffet, who formerly ran pay-per-view for HBO.
"People are getting together to have a great time and we surely need an excuse to have a great time."
The fight will also be seen by millions more worldwide, with promoters claiming it will be available either online or on a TV screen to more than 1 billion homes in 200 different countries.
"If you are in Manhattan or you are on a desert island somewhere, if you have Wi-Fi, you can buy this fight," promoter Dana White said.
Each pay-per-view sale means more money in the wallets of both fighters.
Though estimates vary widely, Mayweather is expected to make some $200 million, while McGregor will likely pocket at least $100 million.
Though ticket sales have been slow in Las Vegas - largely because of astronomical prices - the fight is shaping up as must-see TV at a price of US$99.95.
Who did it: McGregor v Mayweather
People are expected to buy the fight in record numbers, with many sharing the cost of the telecast with friends and family they invite over.
Industry observers say it's hard to judge how many homes will buy a pay-per-view until the day of the fight many times, as people often buy late.
But the anecdotal evidence - primarily the chatter on social media - indicates a good likelihood of it smashing the 4.6 million record of pay-per-view sales set by the Mayweather-Pacquiao fight.
Stephen Espinoza, who heads sports for Showtime, which will televise the fight, said the very nature of the fight - a matchup between a UFC star who has never boxed as a pro against one of the greatest fighters of his time - will drive the pay-per-view sales.
"We believe this is an unprecedented event, quite frankly no one knows what to expect," he said.
"The element of these two outspoken personalities in one unprecedented event is compelling."
