Notice period

Dear Sir/Madam, I have joined a company before 3 months and i have resigned 20 days ago in written to my reporting manager and HR manager through mail. I was taking regular follow up from them but they were least interested in response to me. Today my reporting manager replied with acceptance of resignation letter and ask me to serve notice period of one month from date of acceptance of resignation. It is clearly mentioned in my offer letter that you can terminate your duty with written one month notice to employer which i ready to serve but they ask me to serve notice period from date of acceptance not from date of resignation. I have company assets like credit card, laptop, etc. Please suggest me to what should i do. My next employer is not ready to wait after 30 days of notice period, they ask me to terminate offer letter if i will delay in joining. I need to join next company just after competition of notice period end. Can i leave my current company after 30 days of notice period from date of resignation?