Reports of tension between the pair emerged last weekend after Contostavlos accused Rowland's contestant Misha B of bullying other contestants on the show.
The N-Dubz singer has now said that she has not spoken to Rowland since the incident and feels she has done nothing wrong.
Contostavlos told The Mirror: "[Other] than what you see on air, Kelly hasn't spoken to me backstage. At the end of the day it is a competition and I'm getting on with it.
"She can talk to me and we can sort it out, but if she doesn't want to sort it out we don't have to talk. I'll just get on with it.
"I don't feel I have to make the first move or apologise because I have done nothing wrong."
Contostavlos also defended her decision to confront Misha B live on air over claims she has been bullying girlband Little Mix.
"The truth is, on that day, that was the second incident I had had with [Little Mix] where they had come into my dressing room crying that morning over something Misha had said to them," she said. "If I've got my acts, four young girls, coming to me in tears, I was wound up that day and I thought I am going to go out there and defend my acts."
She added: "I was a little bit surprised by Kelly's reaction but, do you know what, I'm not upset by it."
Rowland will not appear at this weekend's live shows after developing a throat infection during her trip to Los Angeles. 2008 X Factor winner Alexandra Burke will serve as a guest judge in her place.
Burke joins Contostavlos, Louis Walsh and Gary Barlow on The X Factor tonight from 8pm on ITV1.
Watch the video for Kelly Rowland's 'Down For Whatever' below: