Peters' resignation comes three days after the NHL and Flames announced they were investigating a claim that the 54-year-old used a racial slur in addressing a player earlier in his coaching career.
"The subject matter we've been dealing with over the last few days is difficult and hard and does not in any way reflect the core values of the Calgary Flames," general manager Brad Treliving said. "It's been a difficult time, but we are going to move forward. (Associate coach) Geoff Ward will be our interim coach. I met with our players this morning and we're ready to move beyond this and focus on the game on the ice."
Akim Aliu, a second-round pick (No. 56) of the Chicago Blackhawks in the 2007 NHL Draft, alleged on social media Monday that he was repeatedly subjected to a racial slur during the 2009-10 season.
Although he didn't mention Peters by name, Aliu played that season for Chicago's American Hockey League affiliate in Rockford, where Peters was coach. It was Aliu's first professional season and Peters' third and final season with Rockford.
"I think in a general sense there's acceptable and non-acceptable behavior. I think whether it be in dressing rooms or in society. We all evolve," Treliving said. "From our standpoint you want people to feel safe, secure in the environment, and I think this is going to be a learning lesson for everyone and hopefully this, as difficult as these days have been, hopefully this is something that can be positive moving forward."
Peters, in a letter sent to Treliving on Wednesday that was shared by Sportsnet, apologized for "offensive language I used in a professional setting a decade ago."
"I know that my comments have been the source of both anger and disappointment, and I understand why," he continued. "Although it was an isolated and immediately regrettable incident, I take responsibility for what I said."
Peters, who was hired by the Flames on April 23, 2018, was 61-37-11 in two seasons with them, including 11-12-4 this season. Calgary finished first in the Western Conference last season (50-25-7) but lost in the first round of the Stanley Cup Playoffs to the Colorado Avalanche in five games.
He coached the Carolina Hurricanes from 2014-18 and is 198-175-64 in 437 NHL regular-season games. Peters made the playoffs in one of his first five seasons.
Ward, who guided the Flames to a 3-2 overtime win at the Buffalo Sabres on Wednesday, joined Calgary last season after spending three seasons with the New Jersey Devils as an assistant. He also was an assistant with the Boston Bruins from 2007-14, helping the Bruins win the Stanley Cup in 2011.
"Geoff's an experienced guy. He's been around. Part of what we're going through right now is some turbulence. I think stability is important," Treliving said.
"But Geoff is a solid man, solid coach, knows the players, good relationship with the players. ... When this thing happened, I felt Geoff was the right man."
After Peters resigned, the NHL released the following statement:
"The League has been in regular communication with Calgary Flames management and our review of this serious matter is ongoing. There are meetings scheduled with relevant individuals -- including Akim Aliu -- in the coming days. We will have no further comment at this time."
NHL.com independent correspondent Aaron Vickers contributed to this report