Bruce told the Wigan Evening Post: "That story is just nonsense.
"Mario enjoyed an unbelievable first season with me at Birmingham - his combination with Jermaine Pennant on the right was as good as it gets.
"Mario got the brunt of the criticism, and so did I.
"But there has never been a problem between myself and Mario.
"And when I spoke to him on Monday morning, I told him he would continue as captain.
"After relegation at Birmingham, I had to shake the whole team up.
"The big earners had to go, and Mario was one of them.
"I had to sell Emile Heskey too, so perhaps there was an element of hindsight there."
Melchiot also said: "There is no problem. We had a good chat this week and everything is how it should be. Steve will be trying to put things right from the start. But he'll have to get to know everybody because except for myself and Emile, he won't know the squad.
"Maybe they won't be new players to him, but they'll be new personalities. Steve is a strong character, and he will get what he wants across to the players. He'll make sure the club gets the best out of us. We are starting a new chapter so we have to look forwards."