McGregor, the massive underdog for this weekend's bout, restricted himself to verbally abusing a heckler in the audience.
In stark contrast to their lurid, trash-talking global press tour last month, a subdued McGregor and a stern-looking Mayweather spoke respectfully as they looked ahead to Saturday's 12-round boxing contest at the T-Mobile Arena.
Mayweather, who bombarded McGregor with expletives and homophobic slurs during last month's frenzied publicity blitz, did not swear once during Wednesday's news conference.
McGregor, the massive underdog for this weekend's bout, restricted himself to verbally abusing a heckler in the audience who predicted he would be knocked out.
McGregor faces his first ever professional boxing contest against Mayweather, the undefeated former welterweight king who has come out of a two-year retirement to take on the Irish mixed martial arts star.
However McGregor, the 29-year-old from Dublin, insisted he was ready to stun the world of combat sports by upsetting Mayweather, who would improve his record to a perfect 50-0 with a win.
"Been to a lot of these crazy press conferences," said McGregor, a two-time UFC world champion. "This is a lot more subdued. More business-like, the way I like it."
"We are prepared for 12 three-minute rounds of non-stop pace. We are prepared, I will put pressure on him and break this old man. Trust me on that."
"I don't see him lasting two rounds. I feel I have the decision to end it inside one."
"Keep your hands up, keep your hands down, I don't care, I'm going to break through whatever's in front of me."
Mayweather, 40, looked relaxed throughout, even taking time to quietly admonish members of his entourage shouting at McGregor.
And rather than the abuse of last month, Mayweather praised McGregor as a "helluva fighter, a stand-up guy and a tough competitor."
"It's not going to be an easy fight," Mayweather said. "It's going to be blood sweat and tears. "He's the best at what he do, I'm the best at what I do. It comes down to the two competitors going out there and displaying our skills."
But Mayweather's words came with a warning for McGregor.
"After 21 years I've been hit with everything and I'm still right here," Mayweather said.
"And if you give it, you must be able to take it."
"Anything and everything in boxing that can be done, I've done it. I was born a fighter, I will die a fighter. He's going to bring his best. But it's not going to be easy, Conor."
McGregor is hoping his punching power can catch Mayweather out on Saturday. But the American veteran warned he had faced plenty of hard hitters before.
"Manny Pacquiao got bombs, Canelo (Alvarez) got bombs, Shane Mosley got bombs. But remember this -- I got a great chin. And the same way you give it, you've got to be able to take it."
The showdown between Mayweather and McGregor was confirmed in June after a protracted guessing game about whether the two fighters from different sports would meet.
Saturday's bout could become the most lucrative fight in history according to Showtime Sports television executive Stephen Espinoza.
Mayweather could add another $200 million to his career earnings depending on pay-per-view sales while McGregor, who only four years ago was a struggling former plumber's apprentice living on welfare, could collect $100 million.
This will be the most widely distributed pay per view in history," Espinoza said.
"That's not hyperbole that's fact. We are well on the way to a record-setting event."