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BOSTON The New York Times Co. will resume negotiations with The Boston Globe’s largest union, more than a day after talks to cut millions of dollars from their contract ended at an impasse.

Times Co. spokeswoman Catherine Mathis said talks would resume Tuesday at 5 p.m.

The company had set a deadline of midnight Sunday to reach agreement with its unions to make $20 million in cuts and avoid the newspaper’s closure.

The Guild, which represents about 700 editorial, advertising and business employees, said it offered more than the $10 million in concessions demanded by the company. But the offer did not include an end to lifetime job guarantees, and the negotiations ended early Monday without an agreement.

A message left for the union was not immediately returned.