I'm working as a contract employee for X company and working in client location

Hi Sir, I'm working as a contract employee for X company and working in client location from last 8 months. As per my offer letter received from my contract employer , it clearly says below lines- "Your services are liable to be terminated by 30 days notice on either side or payment in lieu therefore.The notice pay amount shall be calculated on your last drawn basic salary. You shall also be bound to give similar notice of resignation at the time of leaving." Now I got offer from some other company and I kept my resignation email yesterday to my employer saying I'm resigning from today and will serve 30 days of notice period from today. He didn't pick my call yesterday and didn't respond to my email also. Today I sent email by copying HR manager. Now he replied to my email saying we spoke with your client manager, he's not willing to accept your resignation.... What I have to do now? Do I need to follow the notice period of 30 days as mentioned in Offer letter or do I need to wait for my employer to accept and give my last date. Moreover I have clearly given last date to my employer by considering 30days notice period as mentioned in Offer letter. Please advice. If I don't get relieve by 30 days I may get some problem in my new company.