BOSTON — As an employee revolt at a New England grocery store chain headed into its fifth week, the governors of Massachusetts and New Hampshire took the unusual step of personally stepping into negotiations aimed at ending a standoff threatening the future of the popular low-priced supermarkets.

Massachusetts Gov. Deval Patrick and New Hampshire Gov. Maggie Hassan participated in negotiations Sunday with the owners of the Market Basket chain – feuding cousins Arthur T. Demoulas and Arthur S. Demoulas – as well as several other shareholders.

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Market Basket employees and supporters jeer at a car driving into the supermarket's headquarters in Tewksbury, Mass., on Monday. The Associated Press

The chain has about 25,000 employees and 71 stores in Massachusetts, New Hampshire and Maine.

A long-running feud between the two cousins culminated in the ouster of Arthur T. Demoulas as CEO in June. His firing prompted worker protests and customer boycotts that have brought the private company to a virtual standstill.

The company has lost millions of dollars over the last four weeks as warehouse workers have refused to make deliveries and customers have shopped elsewhere in a show of support for the employees, leaving the stores with only a trickle of business.

Arthur T. Demoulas has offered to buy the 50.5 percent of the company owned by his cousin and other relatives on his side of the family.

Heather Nichols, a spokeswoman for Patrick, said the two sides made “real progress” on the terms of the sale and operating control of the company during the negotiating session. She said the governors are encouraged that a resolution may be “within reach.”

Hassan’s press secretary, William Hinkle, said the governor is hopeful that the leaders at Market Basket can resolve the standoff.

“Market Basket is a significant business in New Hampshire, and its role as an employer for thousands of dedicated employees and as a provider of affordable groceries for its customers impacts our economy and communities in many ways,” Hinkle said in a statement.

Neither Demoulas cousin commented.

The company’s board of directors met Monday, but the board did not release any details on the status of negotiations.

Employees continued to picket near the company’s headquarters in Tewksbury.

The company’s troubles have trickled down to its suppliers. On Monday, one of the chain’s seafood suppliers said it has ended its business relationship with current Market Basket management.

In a letter posted on Facebook, Boston Sword & Tuna Chief Executive Tim Malley said his company suffered a significant loss in income after Market Basket warehouse workers stopped accepting deliveries. Malley said the company’s new management was sympathetic, offered to pay part of its losses and said they had already started hiring replacement staff for the warehouse.

“We think the time has nearly run out for saving this great institution and all those who depend on it. … In our opinion, the only way forward is for the fired associates to come back,” Malley wrote in the letter.

A spokesman for Market Basket said the shutdown of the warehouse and distribution system has affected all aspects of company operations, making it difficult for customers and vendors. The company is focused on trying to find solutions that address its distribution system.

Last week, the company warned warehouse workers to return to their jobs by Monday or face termination.

But Malley said that as the dispute dragged on, he watched as Market Basket’s new CEOs “made one incredible strategic blunder after another.” He said that after his staff complained to Market Basket about not receiving payments, his company was overpaid twice, once by about $83,000, and more recently, by more than $415,000.