The former CEO of Market Basket says that despite his willingness to pay the asking price for the supermarket chain, his rivals on the company’s board of directors continue to rebuff him.

In statements issued over the weekend, ousted CEO and minority owner Arthur T. Demoulas said that while negotiations continue over his proposal to buy the Massachusetts-based company, board members are offering “counterproposals that have been laden with onerous terms that are far beyond comparable transactions.”

Demoulas Supermarkets Inc. owns 71 New England grocery stores, including one in Biddeford. The stores have been virtually empty since angry employees initiated a successful customer boycott following Demoulas’ June 22 ouster.

Demoulas said that while he does not believe “a war of press releases and statements is helpful to this very serious situation,” he was compelled to respond to “false information” circulating in the media.

He said board members Sunday did not accept his offer to purchase Market Basket for their asking price, which reflects the value of the company before the customer boycott and subsequent staff reductions. Instead, they demanded additional conditions that Demoulas did not specify but said were unacceptable.

Still, Demoulas said he is hopeful that he and the board will reach an agreement “on reasonable terms before it is too late to save the company.”

Supermarket analysts say it is imperative that the board, which is majority-controlled by Demoulas’ rival cousin Arthur S. Demoulas and his immediate family, act quickly to stop Market Basket from hemorrhaging cash as the customer boycott continues.

On Friday, the board said in a news release that it had asked Demoulas and his ousted management team to return in lesser roles to help stabilize the company. They refused.

Many customers have said they would continue to shop elsewhere unless Arthur T., a beloved figure among Market Basket employees, was reinstated as chief executive.

The majority owners have said they are entertaining multiple offers to buy out their share of the struggling company.

Aside from Arthur T. Demoulas, likely buyers include chains from other regions looking to break into the New England market, and existing New England chains such as Scarborough-based Hannaford Supermarkets.

However, some analysts have said that without Arthur T. back at the helm, it would be difficult to restore customer and employee confidence in the company.

Thousands of employees and their supporters have been participating in demonstrations outside the company’s headquarters in Tewksbury, Massachusetts, and calling for him to be put back in charge.

Critics of Market Basket’s new co-CEOs, James Gooch and Felicia Thornton, include Biddeford Market Basket director Micum McIntire, who Saturday posted an open letter to Gooch and Thornton, asking for their resignations to clear the way for Arthur T.’s return.

Meanwhile, three members of Market Basket’s board of directors pressed the feuding shareholders to resolve their dispute so the beleaguered supermarket chain could resume normal operations.

McIntire’s letter, a copy of which is posted at the front of the Biddeford store, said putting Arthur T. back in charge was the only way to end the turmoil that was costing workers their livelihoods.

Those workers include roughly 270 part-time employees at the Biddeford store who were told Thursday that they would not be scheduled to work until further notice. In all, Market Basket has about 25,000 employees, the vast majority of whom are part-timers who have been taken off the schedule.

Arthur T. Demoulas is a hero to many in the company because of his employee-friendly demeanor and generous compensation policies. 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.

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.

In a statement Friday, Arthur T. said it is time for the board members to put aside their differences and return Market Basket to normal operations under his leadership.

“This is far too serious a situation for these games and attempts at window dressing,” he said. “It is a serious issue that deserves a serious solution.”