Muller begins his first NHL head coaching job with a slumping team that has made one playoff appearance since 2006 and has lost 10 of 13 games.
He was in his first season coaching the Nashville Predators' AHL affiliate in Milwaukee after spending five seasons on the Montreal Canadiens' staff. He played 19 seasons in the NHL, made six All-Star teams and led the Canadiens to their most recent Stanley Cup in 1993.
"It's very simple: you've got to get guys to believe in the system," Muller said. "You've got to get them to believe in being accountable for each other. And if you can come every night and you create that culture, and you give them something, a way to believe in how they play and why you're going to win that night, I think that's what players want."
Carolina dropped to 8-13-4 following Sunday night's 4-3 loss at Ottawa, its third in a row. The Hurricanes are 14th in the Eastern Conference - but only five points out of the No. 8 spot - and play Southeast Division leader Florida on Tuesday night to begin a three-game homestand.
"You certainly don't give up on the season at this point in time, and as bad as we've been over the last five weeks or six weeks, we're really not far out of being in the thick of things," general manager Jim Rutherford said. "A new coach can't come in and just put his new system in in a morning skate and all of a sudden make things better.
"We may win tomorrow night, we may not, but really what I want to see is on a consistent basis, we have that work ethic," he added. "And when we get to that consistent basis, the wins will come and they will come in streaks."
Rutherford said he began considering changing coaches roughly a month ago during the team's slow start and reached his decision following the Hurricanes' listless 4-0 loss at Montreal on Nov. 16.
Rutherford said he and Muller - whom he said was the top name on his short list - had been in contact for little over a week, and he discussed the job with Jeff Daniels, coach of the Hurricanes' AHL team in Charlotte but ultimately preferred to go outside the organization.
Maurice became the second coach in his division to lose his job Monday. His firing was announced about 90 minutes after the Washington Capitals fired Bruce Boudreau and replaced him with Dale Hunter. That means every team in the division except Tampa Bay - which hired Guy Boucher in 2010 - has changed coaches since last spring.
Maurice's assistants - Rod Brind'Amour, Dave Lewis and Tom Barrasso - were retained and will work for the 45-year-old Muller, a star center picked behind Mario Lemieux in the 1984 NHL draft who went on to score 30 or more goals five times and post seven 70-point seasons.
He has been asked to revive a Carolina team that ranks 28th in the league in goals allowed, giving up an average of 3.24, and has one of the worst power-play units in the NHL, scoring on just 12.2 percent of its chances with the man advantage.
"I'm just honest, straightforward," Muller said. "I believe in accountability. I believe that it's a tough league, you've got to work hard, and if everyone's accountable to each other, everyone buys into a system, it's amazing what you can accomplish."
There may be more changes ahead for the Hurricanes. Rutherford wants to add a top-six or top-nine forward and could try to deal a defenseman.
"We're a long ways away from being the team we need to be," Rutherford said.
Maurice, who helped shepherd the club's move from Hartford to North Carolina in the late 1990s, returned to the Hurricanes in December 2008 when Peter Laviolette was fired. He guided their run to the 2009 Eastern Conference final, the club's only postseason berth since they won the Cup in 2006.
Before that, they hadn't reached the playoffs since Maurice led them to the 2002 Stanley Cup final - the highlight of his first stint with the team. He was first fired by Carolina in 2003-04 following an 8-14-8-2 start.
Maurice received a three-year contract in 2009 that ran through this season. His combined record with the team was 384-391-145, and his career record of 460-457-167 includes two years with Toronto sandwiched by his stints with Carolina.
Maurice did not immediately return a text message left Monday by The Associated Press seeking comment.
Maurice holds the Hurricanes' career coaching record with 25 playoff victories. The 2009-10 team set a club record with a 14-game winless streak, last season's group finished one victory shy of making the postseason when it lost the finale on home ice and this season's team has shown virtually no consistency.
"When you put a group of guys together at the start of each season, you watch to see the team come together and to jell," Rutherford said.
"Some teams do, and some teams don't. And at this point in time, this team hasn't - for whatever reason. ... From a team-concept point of view, even in years we haven't made the playoffs ... we've been very fortunate with real character guys that wanted to win at all costs. And at this point in time, this group of guys don't. Haven't.
"So that's what we'll see here. Can Kirk pull these guys together and get them to step their game up? And if he can, that's good for this group."