Barton is serving a three-match ban after punching Pedersen in the stomach during Rovers' 2-1 victory at St James' Park last week.
It is the latest in a string of controversial moments during Barton's career but Pedersen spoke up for the 28-year-old, who issued a statement of apology before phoning the Norwegian personally on Friday.
Pedersen said in the Lancashire Telegraph: "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.
"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."