Avery exchanged words and shoves with Blake and his Toronto teammate Darcy Tucker during warmups before New York's 3-2 shootout victory over the Maple Leafs on Saturday.
The FAN 590, an all-sports radio station in Toronto, reported Monday that an unnamed Rangers player said Avery started the pregame scuffle with comments directed against Blake, who was recently diagnosed with a form of leukemia.
"I am extremely upset and hurt that false and damaging comments were attributed to me regarding Jason Blake," Avery said Tuesday in a statement released by the Rangers. "I made no such comments. I have lost two grandfathers to cancer and have been a consistent contributor to multiple cancer-related charities, first and foremost, Hockey Fights Cancer."
Avery is considering legal action against the radio station.
"I am unable to comment further, as the matter is now being addressed by legal counsel," the statement concluded.
Avery met with NHL disciplinarian Colin Campbell on Tuesday in Toronto to discuss his altercation with Tucker, and both players and teams were fined by Campbell later in the day.
The Rangers were given a $25,000 fine, while the Maple Leafs were hit with a $10,000 penalty. Avery will have to pay $2,500, and Tucker was slapped with a $1,000 fine.
The pregame confrontation seemed to be sparked by Avery, who was yelling at Tucker before shoving Blake, who is playing while being treated for his illness. Tucker then slashed Avery before they got face-to-face in a heated exchange.
A week earlier, Avery -- just back from a 10-game absence because of a shoulder injury -- was involved in another pregame skirmish when he jawed at New Jersey Devils goalie Martin Brodeur. Devils forward David Clarkson stepped in then.
"The unprofessional conduct of Avery in initiating this altercation, less than a week after being involved in an incident in the pregame warmup against New Jersey, is the basis for this discipline," Campbell said. "Tucker also bears some responsibility for his inappropriate response.
"Both organizations must also be held accountable for the players' actions."
The longtime adversaries, known as much for their agitating abilities as their on-ice prowess, were sent off together in the first period for unsportsmanlike conduct and fought eight seconds after they left the penalty box.