The pair will meet for the WBC heavyweight title at the Staples Center in Los Angeles on December 1.
After the initial question and answer session went without too much trouble, Wilder accused Fury of being nervous as the Manchester boxer was taunting the American over his appearance and skinny stature.
Fury then pushed Wilder and as Wilder launched for Fury, with the security staff between them, the Brit shadow boxed and shouted: "Any time of day, seven days a week, twice on Sunday. Bring it on, you big s***house.
"He needs all his men I don't need nobody.
"I came to America on my own, I stand my ground against any man born from his mother. Come on, you big dosser."
It was at that point that the press conference was abandoned.