General manager Jim Nill said Tuesday that Peverley is in stable condition and has been communicating with teammates and friends since he was admitted into hospital Monday night. The Stars' game against Columbus was postponed in the first period after Peverley went down on the bench, stunning the crowd and players.
Nill said doctors are focused on finding a long-term solution to Peverley's irregular heartbeat. The condition was diagnosed in training camp, and he underwent a procedure that sidelined him for the preseason and the season opener.
Peverley, 31, also missed a game last week in Columbus because of the effects of the condition. He played in two games before Monday night.
Meanwhile in Montreal, Canadiens forward Brandon Prust said Peverley has the support of the entire NHL.
"I think everyone in the league is thinking about him and praying for him," Prust said. "It's always really sad to see, it kind of breaks your heart."
Prust said there are lessons to be learned from this situation.
"We have good doctors in this league and we're very well taken care of," he said. "So if they say he's good to go, you've got to imagine that he's good to go.
"But obviously, there was something missing there and this is something we have to learn from. I'm sure the doctors will learn from and it's something we're going to have to be more cautious about now."