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NEW YORK -- The NHL said Wednesday it has handled a dispute between the Toronto Maple Leafs and Vancouver Canucks and considers the matter closed.

The league announced it had fined the Maple Leafs an unspecified amount because coach Ron Wilson had "violated the provisions . . . relating to inappropriate public comments by speaking generally to his Club's potential interest" in Canucks twins Henrik and Daniel Sedin.

In a statement, NHL deputy commissioner Bill Daly said the Maple Leafs would face additional penalties if they conducted "future inappropriate conduct" against the Canucks.

The feud between the two clubs began in June, when Wilson was quoted talking about his team's possible interest in the Sedins, who would have been free agents July 1 (they re-signed with the Canucks, each receiving five-year deals worth $30.5 million).

It is against league rules to talk about interest in another team's players while they are still with that team.

Then, Canucks general manager Mike Gillis became furious when he recently heard the comments made by Leafs counterpart Brian Burke. During a taping of a Leafs entry draft documentary, Burke reportedly said Gillis was pursuing the second overall pick owned by Tampa in order to draft Swedish sensation Victor Hedman, and that the Canucks were offering defenseman Kevin Bieksa, forward Alex Burrows and the Canucks' 26th overall pick.

"There are certainly some issues that the league needs to take control of when players' names are being thrown around," Gillis told Vancouver radio station the Team 1040 this week.

However, the league said it found no evidence to back the Canucks' claims that Burke had violated the NHL's rules regarding tampering, calling the mention of the Sedins on the documentary "a brief reference."

Daly said both teams have been warned not to make any public comment regarding the issue.

"From the league's perspective, this matter is closed," Daly said. "We will make no further comment."

Pierre LeBrun is an NHL writer for ESPN.com.