Since the contract provides for a notice period of 60 days from either side the same remains sacrosanct. As per the facts furnished the employee is willing to purchase the notice period of 30 days in addition to the 30 days notice given by him. A lot hinges on the contract of employment in such a case.
There has to be a threadbare perusal of the clauses mentioned in the contract of employment to ascertain whether the employer can refuse to give the relieving letter on the ground that the assignments given before the notice period have not been completed by the employee. Unless and until there is an express mention in the contract to the effect that the assignments started before the notice period have to be completed it is legally not permissible for the employer to withhold the relieving letter.
For the employee the legal remedy begins by serving through his lawyer a legal notice on the company demanding the relieving letter be issued to him. If the legal notice proves futile then litigation can be initiated before the Labour court.