Did you tell him about your offer in new company or not? In spite of sending two mails to your present boss, he does not want to relieve you from the services of company. It means, he requires your presence and as such he does not want to relive you. Do one thing, meet him in person and tell him about your personal problems or offer which you got in else where and tell him if he gives same package or designation which you got an offer from new employer, then you would continue or else leave present company. Then he has two options either to enhance your current pay with designation which you got an offer from new employer or else to accept your resignation without making any protest.
In spite of above, if he does not want either to relieve you or enhance your current package, then you give one more resignation by giving a notice as per your appointment order or make payment in lieu of notice to get the relieving order. Even if he does not want to relieve you, tell the same to new employer and if he agrees to take you without reliving letter from this company, you can go and join there. Thereafter, you need not worry about the terms of appointment order and you can simply leave the services of your present company
Thank you very much for your suggestion:
The following points will clarify my stand:
A.I am resigning not because of dissatisfaction regarding the pay package but because of bad organisation culture and work ethics.
I have seen recruitment of employees without any sense and terminating them abruptly.
I have witnessed my ex-boss resigning after serving the company for 20+ years after pressure from higher management in the pretext of organisation restructure.
B.Since last 6 months they have not given me any concrete KRAs which can be measured absolutely.
C.The present boss is trying to keep me promising they would give me important assignments,he would take me with him etc etc which are vague and is not concrete in any respect.
1.I have send the resignation mail using my offical mail and the boss's reply was "Not accepted."
2.I don't have any dues towards the company like loans etc.
3.Never ever in my tenure of 2.5 years they have served me any warning letters,notices of performance improvement plan.
4.My notice period is of 60 days as per the appointment letter. I have given them a notice period of 20 days and the balance 40 days would be adjusted against the accumulated leave.
5.Currently I am not associated in any important project/groups etc.
6.I have clearly intimated HR regarding my resignation and also asked him to list out the documents that I have to submit.I have also clearly intimated the last working day.
In closing, reiterate that you enjoyed the stint and you are devastated at leaving a place you considered a second home but that you hope to return some day, equipped with much better skills and take them to the next level.
Copy (Cc) your HR personnel as well as the manager's boss so everyone is aware.
Hope this helps