Learned Mr. Chugh and Mr. Thukral have given valuable advice. Kindly follow it.
You should have addressed your notice of resignation to the good offices of your appointing authority, MD, Head-HR and not your manager, and should have candidly mentioned the reason of contemplating to resign e.g. issues you have been facing with your manager. Most of the good companies have their internal grievance redressal system.
Your objective is to finalize your next venture within your notice period. You may address another letter giving reference of your notice of resignation and effective date of resignation, and that you shall be serving full notice period, and your last day in office shall be at the end of notice period of 3 months i.e. dated.............
You may cite email sent to you by your manager and mention that you would like to have a written confirmation from competent and good offices the validity of this email say with in next 2 days and if you do not hear you may walk into the good offices and explain the issues you have been facing and announce that you shall be serving the full notice period. Later you may submit minutes of discussion. There is nothing wrong in giving it a try. Majority of the employee shy/hesitate from visiting and approaching the good offices, and their issues do not reach good offices and line management succeed in getting the acceptance of notice/resignation or even termination from concerned personnel in HR designated to sign on these communications.
If you are running short of time you may approach a competent and experienced service lawyer to draft your representation. You can withdraw notice and submit afresh notice.