I'm a bit confused. If I'm not mistaken, All Verizon phones, including the iPhone, run on CDMA not GSM. Therefore, you can't expect to make calls on a GSM network in India with a CDMA handset. Read this article about CDMA and GSM here - It's a simple and basic description of a Verizon iPhone but I'll copy out of the article what I'm talking about:
Can I use my existing AT&T iPhone 4 on Verizon's network?
Unfortunately, the iPhone 4 that is designed for and sold by AT&T will not work on Verizon Wireless' network. The reason is that the AT&T iPhone is based on a technology standard known as GSM, while Verizon Wireless uses a technology standard called CDMA. These are different technologies, and they are not interchangeable. So if you want to use the iPhone on Verizon, you'll have to purchase the new CDMA iPhone 4 designed specifically for Verizon Wireless.
Again, you can't use a CDMA phone (Verizon iPhone) on a GSM network. This is one reason that the Verizon iPhone is not a good world phone candidate as most networks outside of the USA are GSM (I believe).
Full article here: http://news.cnet.com/8301-31021_3-20028159-260.html
Hope this sheds some light about why your phone isn't functioning on a GSM cellular network.