I own a car but do not have US driving license. I've an Indian driving
license and currently in NY. I'm unable to get car insurance from the
major companies for want of US driving license. I working in NY and
have a SSN and on H1B visa. Can anybody suggest a way to get auto
insurance based on my Indian driving license and the names and contact
details of the insurance companies which can provide auto insurance?

Hi Avk123,
These sites may be of interest to you concerning your right to use a
foreign driver's license as a resident of NY:
http://www.brama.com/novakhvylia/messages/2472.html
http://www.frogsonline.com/america/-usa/usa-driving.shtml
http://www.nydmv.state.ny.us/license.htm#driversfromothernations

Scroll down on this site and find what Univ. of Buffalo advises about
car insurance.
http://wings.buffalo.edu/intlservices/drivlicense.html

It appears that you really have no choice but to get a NY license. 
Perhaps you can arrange short term insurance  - for a price -  with
your Indian license.
Don't drive without insurance  - Murphy's law, not just that you might
have an accident, but that the police will ask to see your license,
car registration and evidence of insurance coverage if they stop you
for anything else.

Good luck, Myoarin