The 2003 Nextel Cup champion said that if Edwards, who has left him several phone messages, wants to apologize for his behavior following Sunday's race at Martinsville Speedway, he needs to do it with action on the track, not words.
"It helps to get an apology," Kenseth said Friday at Atlanta Motor Speedway. "The main thing is, actions speak louder than words. Anybody can call and say the words. I've heard them actually a lot of times.
"You can go run into people and walk up the next week and say, 'Hey, man, I'm really sorry.' And then you can run into him again the next week and say you're sorry. And then you can do that again. Well, pretty soon when you walk up and say you're sorry, you say, 'OK, he doesn't mean that.' "
Edwards said that is Kenseth's decision, but he would like to clear the air.
"My belief is that we should try to work it out,'' he said. "I called him. If he doesn't want to, that's his prerogative. He can do that.''
Kenseth was preparing to do an interview with The Speed Channel shortly after Sunday's race when Edwards walked up, pushed him backward and cocked his right arm as though he were about to throw a punch.
Kenseth called the behavior erratic, noting that only minutes earlier Edwards was talking to members of his team and former teammate Jeff Burton and smiling as he did television interviews.
"I thought that was a little strange," Kenseth said.
Kenseth and several of his Roush teammates, as well as several former teammates, said they've seen this "Jekyll and Hyde" demeanor before.
"I was a little surprised to see what I saw there," Kenseth said of the incident, which was caught on film. "That's a side I see of him every once in a while that maybe some people see and other people don't."
Kurt Busch, who left Roush after the 2005 season, said he's seen that behavior from Edwards all along.
"He gives you that smile like he's always got something under his breath," Busch said.
Burton, who left Roush midway through the 2004 season, said Edwards crossed the line.
"It shocked me, it surprised me, it disappointed me," he said. "It crossed the line, no question. It probably surprised Carl, too. I don't think Carl went over there with the intention of that happening.
"This is an emotional sport, and when you care about it, things happen that you wish hadn't have happened. That's what I suspect happened here. I suspect it got out of hand, and if Carl had it to do again, he wouldn't do that again, I suspect. I'm going to give him the benefit of the doubt that that's what happened," he said.
Edwards said it's been interesting to hear all the opinions about him this week.
"People don't always understand what's going on and what's really happening,'' he said. "And I can say that I really learned how people felt about me, which is nice, because it definitely seems, from what I've learned, that a lot of people don't mind walking around feeling a certain way about you, and they don't say how they feel until it's popular to say it.''
Team owner Jack Roush has been actively involved in trying to resolve what appears to be a personality clash between Edwards and Kenseth on and off the track.
"I think we have the measure of it," he said. "Certainly, Carl realizes that he wasn't a friend to Matt, and Matt, I think, is anxious to have Carl get some relief from the dilemma he finds himself in.
"We're working our way through the aftermath of the conflict that was regrettable, and I think in the future, in a scenario where there will be conflict and differences of opinion, that we'll be able to avoid that confrontation," he said.
Edwards painted a picture that indicated the problem wasn't just between him and Edwards, that there is an overall lack of communication at Roush. Kenseth disagreed.
"The team is great," he said. "I know there were some comments about team spirit. Right now, honestly, besides the two of us for whatever reason, team morale is maybe not at an all-time high, but it's pretty high."
Greg Biffle and others at Roush agreed.
"It's one of those things where I don't know how to fix that," Kenseth added. "He can tell me whatever he wants, but ... actions speak louder than words. Until you see the actions that it's going to be different, then it's probably better [if we don't speak]."
Edwards stood by his comments that he and Kenseth have barely talked for six months and communication isn't what it should be at Roush.
"I've said what I said about that, and that's how I feel,'' Edwards said.
Edwards did his best to keep the mood light Friday. So did Kenseth.
They just didn't do it together.
Kenseth began Friday's news conference by jokingly referring to the charge he is making in the Chase, when in reality, he is in last place, 462 points behind leader Jeff Gordon.
"I'm pretty sure we're going to win the championship," he said. "We're closing in right on it. A couple of more good weeks like we had at Martinsville, and we'll be right there."
He then closed the news conference by saying, "The whole thing was disappointing. Obviously, it was kind of ugly, but it gave you guys something to talk about all week. I'm really sick of talking about Jimmie [Johnson] and Jeff driving away, leading the points thing."
David Newton covers NASCAR for ESPN.com. He can be reached at firstname.lastname@example.org.