There will be more talks today. The union said the meeting would provide it with the opportunity to offer an alternative concession package to the $10m the owners of the paper were looking for.
The Boston Globe's Newspaper Guild president said: "Talks are continuing. They will resume again on Tuesday."
Last week after union members voted against the $10m cuts, the New York Times Company said it would impose the cuts anyway.
It then revealed that it had hired investment bank Goldman Sachs and effectively put the Boston Globe up for sale.
There are reported to be three possible bids interested in buying the loss-making paper.
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