Look at US companies that have physical locations near you. (You didn't say where you live in India.)

For example, when I was at EMC, we had a very prominent office in Bangalore, and "hired" people from that office instead of hiring contractors.

These physical locations are known as captive centers/global-capability-center...! And these companies are least likely to give me contracts/employment in my situation - I live away from metros in Central India (MP).

I'm looking for remote, but am open to partly visiting the client side at their expense - this was something very common with the consultants that my US employers hired in the US.