Burke refused to take questions from media after the event.
Flames president and CEO Ken King issued a response to Burke's comments.
"Brian Burke runs Hockey Operations for the Calgary Flames and he and many Calgarians have strong views about this topic. However, he is not our spokesperson regarding a new events centre for our city. We remain committed to our dialogue with the City and very optimistic we will get to a positive conclusion. We admire everyone's enthusiasm on this subject."
Scotiabank Saddledome has been the Flames' home since it opened and is the second-oldest arena in use in the NHL. Madison Square Garden, home of the New York Rangers, opened in 1968, but a $1 billion renovation was completed in 2013.
Scotiabank Saddledome was flooded to the eighth row of seats in June 2013, but the arena was repaired in time for the Flames to start their preseason schedule on time in September.
King said the Flames moving was an option in a letter to fans posted to their website April 2.
"In response to a question, are you going to use the threat of moving as a tactic, I said we would not. I also said we would 'just move,'" King wrote. "The facts are we need a solution and if it is deemed that there is no made-in-Calgary solution we will have to make a decision at that time, which logically could include deciding to move the team. It is merely one out of a few possible outcomes if we are unable to reach a deal with the city that will work for both sides."
Commissioner Gary Bettman has said the Flames need a new arena.
"I think everybody knows the new arena is important on a whole host of levels for a whole host of reasons," he said March 15 while in Calgary. "You've got to get from here to there, and since I tend to be an optimist by nature I'm hoping that on both sides, not that there are sides, but the city and the Flames can figure this out.
"It's important. It's vitally important that it gets done."
In August 2015, the Flames unveiled CalgaryNEXT, an $890 million plan for a new hockey arena, covered football stadium and a multisport field house in Calgary's West Village, and another location just north of the Saddledome also has been billed as a possible option.
"[Scotiabank Saddledome] was built in the 1980s," Commissioner Bettman said. "They don't build buildings like this anymore. It's a grand old building. It's got a great roof line. It's historic in many ways. But these aren't the facilities that our hockey teams typically have … this is an old, antiquated building.
"And in terms of amenities for the fans, which is the most important thing, it doesn't hold a candle to what's been done in new arenas."
