The Sun reported that the 34-year-old got heckled at London's O2 Arena on Thursday (February 7) after he began crying.
The Liverpudlian singer, who came third in the competition last year, was alleged to have spoken about his "journey" and "ups and downs" twice within a four-song set.
However, tweeting at The Sun's Gordon Smart, Maloney wrote: "wot an absolute crock of s*@t u write in ur column 2day! wen will SUN NEWSPAPER ever print the truth? never learn, lies again!"
He later added: "that's the sun newspaper for u, they hate people from Liverpool end of! xx"
Smart replied: "just landed back from LA. I'm annoyed too. Why your name is even in my column is beyond me you talentless oxygen thief."
Earlier this week, Maloney had a tattoo done on his arm, featuring a microphone and Bette Midler lyrics. The inking was in part a dedication to his late grandfather.
Speaking in a YouTube clip while having the tattoo done, Maloney said: "You forget how many people watch the show and it's like we've got 400, 500,000 people coming to watch the tour."
He also tells the tattoo artist that he gets stopped by fans "everywhere".
Photo gallery - X Factor tour in pictures: