Carey confirmed in July that she would be joining the panel for the next season of American Idol, while Minaj and Keith Urban were announced as new judges on Sunday.
However, previous rumours have suggested that Carey was unhappy about the idea that Minaj could join the show and later reports claimed that the duo had clashed during taping on Sunday.
Carey has now denied the speculation at a press conference in New York, People reports.
"How can we feud in two days?" she asked. "I think a feud takes a little longer."
Meanwhile, Minaj said she is having a "wonderful" time filming the show, while fellow judge Randy Jackson suggested that the panel are getting on well.
"We're having fun, dude," he said. "We've been having a good time. There has been a lot of laughs."
Urban recently described his invitation to join the American Idol panel as an "honour".