Till now, 28 states and UTs have rolled out the law while 8 states are in the process of doing so, he said.
The law was passed by Parliament in 2013 and state governments were given one year to implement the scheme. Since then, the deadline has been extended thrice, with the latest one ending September 2015.
The food law provides legal entitlement to 5 kg of subsidised foodgrains per person every month at Rs 1-3 kg to two-thirds of India's population.
Food Secretary Vrinda Sarup said both Tamil Nadu and Kerala will take more time to implement the law.
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She added that the remaining states and UTs such as Manipur, Mizoram, Nagaland, Arunachal Pradesh and Dadra and Nagar Haveli are laying necessary infrastructure required for implementing the law.
The Tamil Nadu government, which is implementing the universal public distribution system, has indicated that it would roll out the law in July.
To bring in more transparency in public distribution system, he said more than 3 lakh ration shops will be automated by installing 'point of sale' devices by the end of this fiscal year.
Online procurement will be introduced to extend the reach of FCI operations during this budget year to make these more transparent and extend benefits of MSP operations to more farmers.
Digitisation of list of beneficiaries, doorstep delivery of grains and setting up of grievance redressal cell are three basic requirements that are mandatory for states to implement the Food Law.