five-weight undefeated champion Mayweather.
McGregor spoke first as they addressed a packed audience at the Staples Center, with 'The Notorious' taunting Mayweather for his dress sense and reported tax issues.
His opponent then took to the podium to show off a $100m cheque from his last bout and derided the Irishman for his UFC submission loss to Nate Diaz but McGregor was quick to offer up a prediction as to how he thinks the fight will go.
"These boxing press conferences are a completely different setup than what we are used to, but 20,000 people, it is mind-blowing, I am absolutely honoured to be here before you to give you this great spectacle," he said. "And somebody's 0 has got to go!
"There's no other way about it. His little legs, his little core, his little head. I'm going to knock him out inside four rounds, mark my words.
"The movement, the power, the ferociousness - he's not experienced this. He's fought people who have shied away from him. I don't fear this limited set of fighting. This is a limited set of rules that makes this half a fight, a quarter of a fight. If this was a true fight, it wouldn't even take one round.
"What can I say, I'm a young, confident, happy man who has worked extremely hard for this."
'Money' Mayweather hit back at McGregor before the pair squared off and exchanged angry insults again before their respective teams stepped in.
"We know Mr Tapout likes to quit and you will," Mayweather said. "You going out on your face or you going out on your back. Which way you want to go? Which way do you want go?
"He looks good for a seven-figure fighter, he looks good for an eight-figure fighter, but I'm a nine-figure fighter."
The publicity tour moves on to Toronto on Wednesday, New York on Thursday and finally London's SSE Arena on Friday.