The pair squared up after Fury got up out of his seat and asked Wilder to demonstrate his punching power, with the American responding by pushing his rival.
Security immediately stepped in to separate the pair, with the explosive press conference then drawn to a hasty close.
It was a predictably explosive press conference, with Fury almost immediately promising to “smash Wilder’s teeth in” upon taking his seat.
Fury, who has won both fights on his return to the ring, pulled no punches during their heated exchange and his comments infuriated Wilder so much he was forced to push the Gypsy King in return.
“I am savouring nothing, the only thing I am savouring is smashing Wilder’s teeth in,” he said. “All the press are here to see the biggest fight of our generation, you are in for a treat.
“I am in the mood for no messing around, no 15 stone man can beat Tyson Fury. If we fight 30 times I would win 30 times.
“The thing is Bronze Bomber, you big dosser, you are not ready for me. You are going to f*** yourself.
“If I can’t beat you, I’ll kiss your two feet on the floor.”
Wilder responded by asking Fury whether he had “ever looked into the eyes of a killer”.