BOSTON — Union members at The Boston Globe narrowly rejected steep cuts in their pay and benefits Monday, prompting the newspaper to immediately impose even steeper reductions in hopes of cutting $10 million in annual expenses and staving off a shutdown from parent company, The New York Times Co.

The Boston Newspaper Guild, which represents 700 editorial, advertising and business employees, voted 277-265 Monday against the new contract negotiated after the Times Co. said it needed $20 million in annual savings from Globe unions — half from the Guild. Six other Globe unions have approved concessions — but they hinged on the Guild’s ratification of new terms.

The Times Co. had said that if the Guild rejected the proposal, it would try to impose a 23 percent wage cut. It also could follow through on an earlier threat to close the 137-year-old newspaper, which would require giving 60 days notice to employees and the state.

In a statement released after the vote, the Globe said it was disappointed with the outcome and has no “financially viable alternative” but to declare an impasse and impose the deeper wage cut to achieve the necessary savings.

“This evening we have sent a letter to the Guild stating that as a result of the rejection of this proposal, we have reverted to our alternative Final Record Proposal which provides for a 23 percent wage reduction for all Guild members,” the statement read.

The cut would be effective next week. The Globe said the newspaper would be willing to meet with the union this week to review implementation of the cut.

About 80 percent of union members voted on the concessions. Union leaders had presented the contract offer to the union without a recommendation either way.

Union president Dan Totten said the vote reflected the feelings of the rank-and-file and he called for a resumption of bargaining.

“With today’s vote, members of the Boston Newspaper Guild have said that the New York Times Co. must do better than the offer that was presented,” Totten said in a statement.

“The Boston Newspaper Guild is committed to resuming good-faith negotiations with The New York Times Company and Globe management to reach an agreement.”

The contract included an 8.3 percent wage cut, five-day unpaid furloughs and cuts in health care benefits, 401(k) contributions and pensions. It also would have eliminated lifetime job guarantees for 190 Guild workers. Most got those promises in exchange for other concessions in a contract ratified in 1994, shortly after the Times Co. bought the Globe for $1.1 billion.