What is the best way reply to an internship rejection email?

It should start with thanks giving words like i am thankful to you for providing me this kind of opportunity in your organization. You should use polite words in the mail keeping in mind it is a professional world. You should not have bad impression on anyone.

If HR contact you over the phone then update them accordingly or if you received an e-mail then reply them firmly and swiftly so that your future employment opportunity is not missed!

Say only " Thanks to your Reply" 

To be very professional; simple and thanks the sender hoping to meet with each other in the work field. Must put in your mind that always you need to have a good relations in business.