NEW YORK — The NHL and the players’ association stuck to their word and made quick plans to get back to the bargaining table.

After all-day negotiations Saturday, the sides agreed Monday to resume talks on Tuesday in New York. Both sides said the discussions over the weekend were good, creating some optimism that perhaps a deal could soon be reached to save the already truncated hockey season.

The NHL and union hadn’t met since Oct. 18, when each side turned down offers. NHL deputy commissioner Bill Daly and players’ association special counsel Steve Fehr got together by themselves Saturday in an undisclosed location and held productive talks.

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‘‘We had a series of meetings over the course of the day and had a good, frank discussion on the most important issues separating us,’’ Daly said Sunday.

He and Fehr talked on the phone several times during the week and reached enough common ground to make face-to-face meetings possible.

Fehr echoed Daly’s encouraging remarks after Saturday’s get-together. ‘‘Hopefully we can continue the dialogue, expand the group, and make steady progress,’’ he said.

It wasn’t immediately determined whether Tuesday’s bargaining session would involve a large group — perhaps including NHL commissioner Gary Bettman and NHLPA executive director Donald Fehr.

The lockout entered its 51st day Monday.