Notice period increased arbitrarily without prior intimation

I have joined my company one year back with 1 month notice period. recently HR sent a mail saying that the notice period has been revised to 3 months with effective from today. The next day they asked me to sign on the revised clause, i refused and i told it is not acceptable for me. Then HR says that it is already implemented and applicable across the organization whether the employee like it or not. The next day i keep my resignation. But my HR was not ready to relieve me in 1 month. he says now you are under 3 months notice period, so you should serve 3 months notice period. Please advice me whether my stand is correct or not and how can i proceed legally. Also during this notice period revision I have got one offer from other company. Since my notice period is for 1 month, I have got my offer letter to join within one month.