League officials were reviewing the counter-offer and NHL Players Association special counsel Steve Fehr said he expects the two sides to meet again Tuesday, Canadian broadcaster TSN reported.
The union's response came after players spent Sunday looking over the league's proposal of last week, which was submitted in a bid to save the remainder of the 2012-13 season as a Jan. 11 deadline for canceling the remaining games looms.
The lockout reached its 107th day Monday.
Reports indicated the NHL's latest offer put forth some key concessions, including movement on the issues of contract length, compliance buyouts and annual-salary variance, NHL.com said.
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