If there is no written or formal acceptance from company's end towards cancellation of his resignation then it wouldn't be great to be forceful against him to serve new notice period. Company's do not accept verbal resignation, it always has to be in writing similarly retraction needs to be in writing as well. He has a valid point here.
ON HR front, it was good to have a leaving employee take back his resignation and continue but trying ways to retain an employee who no matter what is trying out ways to leave even after showing him prospects ahead then you better should start looking for a suitable replacement than wasting time focusing on problem.
All you can do is list out all the necessary tasks he needs to complete before leaving and ask him for a proper handover. That's all in my suggestion.
From India, Mumbai