Till now, 22 states and UTs have rolled out the law while 14 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 this September.
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.
Of 14 states that have not implemented the Food Law, the minister said Andhra Pradesh and Sikkim have said they will implement the same in December.
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Uttar Pradesh, Meghalaya, Jammu & Kashmir, and Andaman & Nicobar will roll it out in January 2016 while other states -- Gujarat, Kerala, Arunachal Pradesh, Manipur, Mizoram, Nagaland -- will do it by March next year, he added.
In the meeting, a Tamil Nadu government official said it can implement the law in July 2016 since it's implementing the universal public distribution system.
On direct cash transfer of food subsidy, Paswan said, "We are implementing it on a pilot basis in Puducherry and Chandigarh. It is not mandatory for states to implement direct benefit transfer (DBT). It is optional for states if they want to give cash subsidy in some parts of the state."
Addressing concerns of some states on direct cash subsidy issue, Food Secretary Vrinda Swarup said: "We are not forcing states to go for DBT. If they want to implement at urban centres, they have that option."
Till now, e-PoS machines have been installed at over 51,000 ration shops while the target is to cover 1.5 lakh by the end of this fiscal, she said.
The secretary said 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.
She also said the deletion of bogus ration cards in the last two years has helped the government save Rs 4,000 crore food subsidy.
In his inaugural address, Paswan emphasized the need for early implementation of the National Food Security Act (NFSA) by all states and UTs in proper manner.
"14 States/UTs are yet to roll out the NFSA. States must keep in view that it is in the interest of the common people that the Act is implemented without any further delay because not only the people get foodgrains at cheaper rates but also more number of people are covered," he said in a statement.
Those state governments, which are further subsidizing foodgrains, will save on the state subsidy as the issue prices under NFSA are already very low, he added.
"It is to be kept in view that right from lifting of foodgrains from FCI depots, the state governments are responsible to make sure that the foodgrains reach the fair price shops without any leakage and are distributed to the beneficiaries in time," he said.
To ensure all this, states are required to correctly identify the beneficiaries, digitise the beneficiary database and place the same on PDS portal and also to have a robust grievance redressal mechanism, he added.