"Eejit" and "Circus Clown" were the tamest epithets the former welterweight king, who retired from boxing with a perfect 49-0 record in 2015, threw at McGregor, one of the biggest stars of mixed martial arts.
"Gave up not once, not twice but three times," said Mayweather. "Real fighters never give up."
McGregor, a two-division champion in the Ultimate Fighting Championship, has conceded three defeats in 24 bouts, all by submission.
The two men are set to face each other in a boxing ring in Las Vegas on August 26 in what could be the richest fight in history.
Thursday's show at the Barclays Center, home of the NBA's Brooklyn Nets, drew a pro-McGregor crowd of more than 13,000.
It was the third such production in three days, with one more scheduled for London on Friday aimed at pumping up interest in the bout – although both men seemed to be running short of inventive invective.
McGregor eschewed his sharp-tailored suits for a bare chest and white fur overcoat – which he swept from his shoulders as he took the stage to offer a flexed-arm pose that inflamed the crowd.
The Irishman then paced impatiently as Mayweather, draped in an Irish flag, made his way to the stage and they took their positions for the ritual staredown from opposite sides of the podium.
A giant step forward from each had them nose to nose and brought more cheers from the crowd before McGregor launched into a lewd, crude address.
"No one's going to stop me walking around this place like I own it," he said.
Mayweather, meanwhile, was all indifference until it was his turn to speak. After a little back-and-forth with the crowd, he showered McGregor with handfuls of dollar bills from his backpack – a day after McGregor mocked the paltry stash of cash "Money" had brought to their promotional stop in Toronto on Wednesday.
"They're all ones," McGregor said. "Because that's all you're worth," Mayweather replied....