Tyson Fury told Dereck Chisora to forget about a rematch ahead of his weigh-in with late replacement Alexander Ustinov.
Chisora was due to face his domestic rival on Saturday, but he pulled out this week with a broken hand and Ustinov will instead face Fury in Manchester this weekend.
The Wilmslow man reacted angrily to the late withdrawal of his opponent, who he defeated on points back in 2011, and is not interested in a rearranged second bout.
Fury, who tipped the scales at 18st 5lbs, told a press conference: "Chisora had his opportunity and fluffed it up for whatever reason. Now I want Bermane Stiverne, the WBC champion, because at least I know he will fight.
"I am not going to keep giving someone opportunities when I know they are not going to take them, like with David Haye."
David Haye also twice withdrew from scheduled fights against the unbeaten 25-year-old, who doubts whether a dream fight with WBA, IBF and WBO champion Wladimir Klitschko will ever materialise.
The Belarussian, weighing in at 20st, has suffered just one defeat in 30 fights - a stoppage against Klitschko's latest challenger Kubrat Pulev.
The two fighters remained calm as they posed for the customary face-off, with Ustinov claiming he could not understand Fury's threats of a knockout victory.
Reflecting on his new foe, Fury said: "I want to fight for the world title next. I deserve it, I have paid my dues. As far as I am concerned, this guy is better than Chisora.
"He is ranked in the top ten by the IBF and WBA and people are more interested in him than Chisora.
"Chisora is yesterday's man. I am only looking to the future. I am going to beat this fella and send him back to Belarus with a big message for Wladimir Klitschko.
"I don't think Klitschko will ever fight me. That's why I want Bermane Stiverne. I am his biggest payday and he will get the most money he will ever earn by fighting me.
"That's the fight I want, for the WBC title, so let's get it on here in England. I want a world title fight next."