"The fans' fight during the UFC 229 weigh-in ceremony; Khabib was hashing things out with McGregor on the stage, while a man in Conor's shirt was hopelessly losing the fight in the auditorium," an eyewitness wrote.
Several people, including women, participated in the fight.
Security officers were able to quickly put an end to the fighting.
At the weigh-in ceremony, McGregor tried to hit Nurmagomedov ahead of the highly-anticipated fight that will take on October 6, 2018 in Las-Vegas at 02:00 GMT.