BOSTON – Unionized workers for dozens of Shaw’s Supermarkets on Sunday overwhelmingly rejected a contract proposal the grocery chain presented earlier in the day and characterized as its final offer.

The 81 percent vote to turn down the proposal and authorize a strike increased the possibility of a walkout this week involving about 6,000 employees at 39 stores in southeastern Massachusetts and Rhode Island and a distribution center in Maine.

But a spokesman for the United Food and Commercial Workers Local 791 said any walkout would wait until after the sides hold another negotiating session with a federal mediator on Monday.

“We’ll wait to see what developments come from the session,” union spokesman Peter Derouen said.

He said 1,214 members cast ballots to reject the three-year contract offer and authorize a strike, with 197 voting to ratify the proposal.

“Quite frankly, we feel this particular offer was an insult,” Derouen said.

A statement issued by West Bridgewater, Mass.-based Shaw’s after the union vote said the company “has put on the table a very generous offer” that would leave unionized workers “among the best compensated in the industry in New England.”

Balloting by a broad range of full- and part-time store employees was conducted at a hotel in Randolph. A separate vote by 350 workers at a Wells, Maine, distribution center was planned Sunday evening.

The store workers’ vote came hours after Shaw’s Supermarkets presented what it called its “last, best and final offer.” Employees continued working at the affected Shaw’s stores Sunday under terms of a contract that expired overnight.

As votes were being tallied Sunday afternoon, the union received word from a mediator that Shaw’s requested another negotiating session on Monday.

The company said its latest offer includes wage increases in each year of the contract, pension increases, and a choice of four health plans: three Blue Cross-Blue Shield plans and the UFCW health plan.

Derouen said the company’s latest proposal offered few improvements from an earlier version. Talks have been under way since June, with the company’s plans to control rising health care costs emerging as the main sticking point. Other differences remain over wages, work rules and pension benefits.

Shaw’s, owned by Boise, Idaho-based Albertsons Inc., one of the nation’s largest food and drug retailers, says its costs for the union’s health care plan for the 39 stores have risen more than 60 percent in the last three years.

The union has said the company’s original proposal would result in a 27 percent reduction in benefits, and shift thousands of dollars to employee insurance co-pays without increasing wages.