During HR round I was asked to quote a minimum and maximum amount of my expected monthly package. And when I was asked how much of that is negotiable I quoted a low amount (way too low). Regarding the offer letter I have been told that paperwork is in progress. Are there any chances for me to re-negotiate the salary?
Everything is negotiable. However, you have risks associated with renegotiating at this point.
Be sure you have a good "BATNA" - Best Alternative To a Negotiated Agreement (look it up). In other words, are you willing to reject the offer or have them rescind it? If to negotiate further your client may rescind the offer. Is that acceptable? If the rate really is "way too low" for you, then you will be glad to have it rescinded. However, why didn't you already know that? That is the awkwardness of your situation - you should really know your lowest acceptable rate when they ask.
So consider that if they made an offer at your lowest "acceptable" level, you might want to address that now in a different way. You could simply ask questions like, "Hey, since you offered me the absolute lowest that I would accept, when can I expect a raise? And how much is normal? And what is the measure of success to receive that raise?" A company that offers you the lowest rate should expect that you will not be content for long. It may be in your best interest (and theirs) to try things out before paying you at a higher rate.
You could suggest that you have a 90 day review regarding your compensation, since they obviously like you (they are making an offer) but the offer is on the low end. It isn't inappropriate to discuss how and when you should expect raises, bonuses, etc.
Last, you should consider that if this company made you an offer on the very low end of you "acceptable range" of rates, then they may continue to low-ball your pay during your tenure with them. You may want to simply decline the offer, if this is a critical issue for you. If they are simply trying to make sure you are a "good fit" before paying you more, this approach should be satisfactory for both of you.