In a statement, Market Basket board of directors said the terminations came as a result of a recent internal investigation that found the two supervisors engaged in “insubordination, making false and derogatory remarks about the company and people associated with it, and inappropriate communications with colleagues.”

Market Basket fired the executives, Joe Schmidt and Tom Gordon, claiming they worked to spark a widespread work disruption to help protect chief executive Arthur T. Demoulas.

The ongoing battle for control of Market Basket grocery stores appears poised to drag on for more than another month.