It depends on the law of India. I'm not sure, but I believe that you must register the Indian marriage for it to be valid. I've handled a several matters involving Indian nationals and Indian law but, still, I have to doubt myself, as apparently your attorneys in India have filed for a divorce. If the marriage wasn't valid due to the lack of registration, then there would be no need for the divorce.
You may divorce your first wife in the US.
You may legally marry in the U.S. as a GC holder.
So, it sounds like the best way forward would be to dismiss your divorce case in India (that has to happen before you proceed in the American family law courts) and then file a divorce case, here. Assuming it's fairly simple, you can probably be done in a few months. Then, once the divorce is done, you may remarry and teh second marriage will be valid.
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I would make sure you are divorced BEFORE you remarry in the US. You do not say where your spouse is living? In India? If so then finish the divorce in India. If your spouse is living here I would have my Indian counsel dismiss that divprce and then file in US. It seems you should consult with an Indian American lawyer who has knowlede of the Indian law in this area.
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If the marriage was not properly recorded, it could be declared invalid. You need to either get a divorce or have the marriage declared invalid prior to any remarriage regardless of your immigration/citizenship status. These details should not be broadcast over the Internet.
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