I have an Apple ID created in India. I will be living in US now on. So when I try to buy apps from here, I get a reply saying, I need to change my store to US. So do I have to create a new ID or can I in anyway continue with this same ID ?

You can use the same ID but you will need a U.S. based credit or debit card account.

This applies to the Mac App Store as well as iTunes...

The Complete Guide to Using the iTunes Store | iLounge Article

"Although you can browse the iTunes Store in any country without being signed in, you can only purchase content from the iTunes Store for your own country. This is enforced via the billing address associated with your credit card or other payment method that you use with the iTunes Store, rather than your actual geographic location."