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The British pair entered through separate corridors at a Liverpool hotel on Monday and were divided by security for the traditional pre-fight face-off.
Bellew, 34, called Haye "a broken man", as they repeatedly exchanged insults.
Haye, 36, threw a punch at Bellew at a November media gathering and had warned they would need a barrier between them.
WBC cruiserweight champion Bellew will fight at heavyweight for the first time, completing a two-division jump after competing at light-heavyweight as recently as 2013.
Former WBA heavyweight champion Haye has had two routine wins since returning from over three years out of the sport.
The London fighter seemed frustrated as fans in attendance drowned out his comments with songs on Monday - and he responded by insulting those in the crowd and said Liverpudlian Bellew would "need all the support he can get".
An agitated Haye told the crowd: "Deep in all of your tiny minds you know this guy is getting drilled to the canvas pretty fast."
Bellew said: "I am going in with a man who was absolutely fantastic. When he was in his prime, an immense athlete - but the tank is very, very low and it does not last very long.
"When the gas runs out, the big fat Scouser is going to steam through him."
However, Haye's trainer, Shane McGuigan, predicted WBC cruiserweight champion Bellew would be "cannon fodder".
Haye's wins since returning - both inside two rounds - prompted Dave Coldwell, Bellew's trainer, to question if the shoulder surgery he had in 2013 could hamper him in a longer contest.
"When you've had major surgery as an athlete, you are never the same man, you have doubts in your mind," said Coldwell, who once worked for Hayemaker promotions.
"Your surgeon advised you to retire, you come back but you don't know how you will perform on the night."
Addressing his opponent, Bellew added: "I've seen people have the operations you have had. Reconstructive shoulder surgery is a big thing, your right hand becomes a looping right hand."
Bellew holds a record of 28 wins and a draw from 31 fights, with Haye boasting the same number of wins from 30 contests.
David Haye and Tony Bellew were physically kept apart at a heated news conference for Saturday's heavyweight bout at London's O2 Arena.