The board of directors at Demoulas Supermarkets Inc. has promised not to fire any additional employees or close any stores until a sale agreement is reached, according to The Boston Globe and a management-level employee who asked not to be named.

The company, which operates 71 Market Basket stores in New England, including one in Biddeford, did not fire as many as 200 no-show distribution and administration workers on Friday, as it had threatened to do last week, the employee said.

According to the sources, the board has vowed to step up its efforts to reach a sale agreement by the end of this week.

Analysts have said that Market Basket is losing millions of dollars a week and must act quickly to resolve a five-week leadership dispute that has led to employee walkouts and a customer boycott. Thousands of part-time employees, including about 270 in Biddeford, have been taken off the schedule indefinitely.

A spokeswoman for Arthur T. Demoulas, the former Market Basket CEO whose ouster in June precipitated the walkouts and boycott, declined to comment Tuesday on the sale negotiations. Demoulas is one of multiple bidders vying for a majority stake in the company.

Employees and customers are still waiting to find out if the board of directors will vote to sell the company to the beloved former CEO.

The Market Basket saga has dragged on for nearly two months, with Demoulas and his rivals on the board publicly exchanging barbs via news releases and written statements.

Since Demoulas was fired on June 22, hundreds of employees have walked off the job and held mass protests, food deliveries have virtually stopped, and the vast majority of customers have boycotted stores.

Demoulas, whose side of the family owns 49.5 percent of the company, has offered to buy out the majority-owning rival faction of the Demoulas family controlled by his cousin Arthur S. Demoulas for an undisclosed sum. Analysts believe a sale to Arthur T. would revive the business and bring former employees back to the company.

While the board has said it wants to sell to the former CEO, he has described the proposed sale conditions thus far as unrealistic and unacceptable.

Arthur T. Demoulas is a hero to many in the company because of his employee-friendly demeanor and generous compensation policies. He also has instituted across-the-board price cuts that have kept Market Basket prices low.

Shortly after he was fired, some Market Basket employees began walking off the job, including delivery drivers who normally stock the stores with fresh produce and meats. As a result, the stores’ produce and meat aisles have been nearly empty for weeks.

The internal dispute at Market Basket goes back decades. In 2013, the rival Demoulas cousins clashed over the company’s future business strategy. Arthur T. wanted to use its cash reserves to open more stores, while Arthur S. insisted that the money be paid out in dividends to the family-owned company’s shareholders. The dispute ended up in court, where Arthur S. won a judgment to distribute $300 million to the shareholders.