Write a letter to your new employer stating that your inability to join duty on the prescribed date and asking for extra time to join. Give valid reasons for the delay.

Dear Sir,

Many thanks for giving me an opportunity to work with your reputed organization on the post of Project Manager. But unfortunately, due to an emergency at my aunt place I will not be able to join on the committed date agreed between us. This is the reason, I am writing to you now to inform you about my inability to join duty.

Just for your information I have done all the formalities in my current organization to join your company; however, yesterday only I had received a call from my aunt who is staying alone and during the call, I came to know that due to her prolonged illness she would be admitted to a hospital for 2 weeks. As there is no one to take care of her except me, I am planning to take 2 weeks leave and would travel to my hometown.

Probably, I know you had planned work according to my previous committed date and there would be a delay in the overall deliveries. But I assure to your company that I would catch up the overall work by working on the weekends.

I would be grateful to you if you accept my request and provide me an extension to join my work. I am looking forward to hearing soon from you.

Yours faithfully
Rahul