Dana White spoke of his pride in Conor McGregor's performance in his Las Vegas grudge match with Floyd Mayweather Jr, but urged the Irishman to return to UFC for his next fight.

McGregor, the first man to hold belts in two different weight divisions at the same time in UFC, defied the critics to hold his own against Mayweather in his first professional boxing bout.

However, the Irishman ultimately came up short as Mayweather found his composure and range after a slow start to earn a 10th-round stoppage.

White was surprised at the way the bout transpired and, while he has yet to discuss the MMA star's next bout, the UFC president wants to see McGregor back in the Octagon.

"I'm so proud of Conor tonight man. It's not the fight I expected, it's completely different to what I expected," White said at his post-fight media conference.

"I've been back there with him pretty much this whole time and we're not talking about fighting tonight, you know?

"He put on a great performance, we're not talking about fighting. You know how he is. When he's ready, he'll let me know."

"I would rather he did not [box in his next fight]. This is not what he does. He's a mixed martial artist, where he goes in and he fights and he uses all of his weapons.

"And tonight, he was only allowed to use his hands. I think he did great tonight, I don't think there's anything left to prove.

"I would rather he fight in mixed martial arts."