I would like to highlight your words "If in any month...," what do you mean by this term? How many days of delay are you expecting? Many companies follow a certain cutoff date for closing attendance and preparing salaries. As you are aware, salaries won't be disbursed in a single day without checking and closing attendance for all employees. That implies the delay was expected and has been planned in advance.
In such cases, the finance department or HR should circulate an internal memo to all employees through possible channels about this delay in salary disbursement. However, if you are still unaware of the date of disbursement, take a tentative date from the finance department and provide it to employees.
Employee Financial Planning and Stress
As you are aware, every individual plans their financial budget in advance of payday. When they learn that the salary is going to be delayed, you can understand their frustration regarding their personal commitments. This is human tendency, especially in Indian social life; such situations cause people mental stress and lead to a lack of concentration. So, this behavior is expected from them.
Organizing a Meeting
Hence, I agree with the suggestion given by our member SUSHMITA that you should organize a meeting with both parties. Giving fake excuses, such as the company is going through problems or we are in trouble, will not work. However, as she mentioned, the result of the meeting should be communicated in a motivated, well-explained, and convincing manner.
In the future, I would recommend circulating an early notice if you foresee such delays.
Regards