The Market Basket board of directors and suspended CEO Arthur T. Demoulas will take their ongoing dispute to a mediator in September as the latest leadership struggle for the grocery store chain continues.

Demoulas was suspended and other executives were put on paid leave on May 28. According to the board, the group was suspended for allegedly "encouraging a widespread work disruption" to show support for Demoulas.

Joseph Schmidt, director of operations, and Tom Gordon, grocery director, were later fired.

Market Basket leadership fight

The dispute stems from Demoulas' role with Market Basket and who will control  the popular chain of grocery stores.

In a statement, Demoulas confirmed that the parties have agreed "to put the issues between them to a mediator on September 3 in hopes of avoiding litigation and reaching a quicker and amicable resolution that is in the best interest of Market Basket's associates, customers and the communities it serves."

Demoulas' statement went on to accuse the Board of Directors of acting irresponsibly.

"The discussions about a mediation have been going on for more than 2 weeks. And that fact alone illustrates how irresponsible Directors Jay Hachigian, Steven Collins and Michael Keyes were early last week, when they fired Joe Schmidt and Tom Gordon and then promoted a series of employees to take their places," Demoulas said. "This was all done in a clear attempt to get out ahead of the mediation process in an effort to further silence the associates within the company who are demanding the return of the senior management team."

The Market Basket board of directors confirmed that mediation efforts will take place on September 3. But chairman Jay Hachigian disputed Demoulas' accusations.

"The statements by Arthur's spokesperson are not credible and make no sense. I look forward to seeing Arthur in mediation," Hachigian said in a statement.

Who is Arthur T. Demoulas?

Though Demoulas is the CEO of Market Basket, he is a minority shareholder who owns 28% of the company. Three of his sisters each own a 20% share, while the remaining 12% is in a trust for the family's grandchildren.

Demoulas and his sisters were involved in a dispute with their cousin in 2014. The battle for control of the company led to a customer boycott and Market Basket employees walking off the job to defend "Artie T." After six weeks, the dispute ended with Demoulas and his sisters coming out victorious.