Barton is now serving a three match ban after he was picked up on camera punching Pedersen in the stomach during the Newcastle v Rovers game last week.
Barton admitted the incident and issued a statement apologising for his behaviour, then rang the Rovers winger to offer a personal apology to him.
"I couldn't answer the phone at that moment but he left a nice message on my answering machine and I called him up the minute we had finished our team meeting," Pedersen told the Lancashire Telegraph.
"Joey shows that there is more to him than what came out on the pitch the other day, and I really appreciate it. It's not everyone who has the courage to call to apologise after such an episode, but Joey did without hesitation.
"Both me and Joey are professional and fully agree to put this behind us, and that we can laugh about the whole thing next time we meet.''