A driver accused of running down two men in separate hit-run incidents that were "racially motivated" has been denied bail and remanded in custody.

Shannon Marchant, 21, slumped forward in the dock, covered his face with his hands and cried when he looked at his family as magistrate Donna Bakos refused his application for bail in Melbourne Magistrates’ Court on Friday.

"Your honour, if I may,’’ Mr Marchant began once the ruling was made, before Ms Bakos cut him off. "You may not," she said.

As he was led out of court, Mr Marchant yelled to his father: "I will ring you, Dad. We will take this to the Supreme Court, we'll go the whole way, mate."

Ms Bakos said she refused bail partly because of concerns Mr Marchant's parents would not provide adequate supervision and because his mother had contacted a prosecution witness.