Market Basket’s chief executives have told employees through a statement that they “need” workers to return to their jobs on Monday, August 4.

Employees have thus far stayed adamant in their demand that Arthur T. Demoulas be reinstated as CEO, shrugging off previous calls from management to return the business to its normal operations. Co-CEOs Felicia Thornton and James Gooch had said as early as Thursday, July 17, that any employee who does not fulfill his or her job responsibilities would be fired. Most store managers have signed a petition saying they will resign if Demoulas is not ultimately brought back as the chain’s leader.

In the statement, Thornton and Gooch said they expect some employees not to heed their call, and will therefore begin advertising some positions. Douglas Moser, a reporter for The Eagle Tribune, said Market Basket will advertise a job fair in Thursday’s edition of the paper.

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A customer boycott and employee protests have continued at Market Basket this week, while the board considers an offer from Demoulas to buy the company.

Store workers have still been showing up to work during the recent employee and customer action, though they have had little to do at supermarkets empty of customers and some products, and many employees have been protesting outside. The employees who have actually walked off the job have mostly been those who work in headquarters and at the company’s warehouses.

Market Basket job fairs will be held on August 4 and 5 for existing employees looking for a promotion, and August 6 for outside candidates.

The full statement from the co-CEOs:

“We want Market Basket associates back to work and reiterate that they can return without fear of penalty. We again acknowledge and understand how difficult this situation has been for associates. However, we also need to have associates working to support stores, customers and vendors. We need associates to return to work on Monday August 4th. We understand that some associates may choose not to return, consequently we will begin advertising for employment opportunities. Our hope and strong preference is to have Market Basket’s incredible associates return to work. Again, any associate that wants to return will be welcomed and not penalized.”

Check out more of Boston.com’s coverage of the Market Basket saga.