These are the trends of the industry. You shall have to act smart with your employers, and document your interactions.
You have fulfilled your part as per your service conditions and you may resign.
Your new employer is cooperating with you.Probably they need your experience and expertise.
You may brief them and seek their advice and submit your letter stating that you have submitted your notice of resignation as per your appointment terms and conditions for 1 month, and that your employer wanted you to be relieved after 2 months 22 days.You are nearing your notice period date and you shall be joining the company, however you are experiencing some difficulties,as your reporting authorities/HR has stated verbally that they shall not issue you the relieving letter.You may mention that you have cooperated and completed all the tasks assigned to verbally and in writing.
You may mention your superiors and HR contact details and that you shall be able to submit the relieving letter only upon receipt and you shall be able to submit the copy of notice of resignation and final resignation immediately and its dispatch details by registered post and its acceptance upon receipt and you may be inducted based on these documents.
You may write letter to your current employer stating the facts of your notice of resignation, notice period of month, and notice period served as per advice of your reporting authority/HR,and your representation to your superiors/HR mentioning their name and date and that you are resignation may be accepted w.e.f .........and the acknowledgment and acceptance may be supplied to you by registered post.
It shall be better to be clear everything and record in writing.