He also sought a hike in compensation to the families of victims, saying atleast Rs 20 lakh should be paid to the next of kin of those killed.
Paswan, who is a member of the HRD Ministry's Consultative Committee, alleged there are "irregularities in the scheme implementation and corruption is rampant".
"The Centre should take it seriously and implement it properly," he said, asking the HRD Ministry to take steps in this regard.
The Lok Janshakti Party leader claimed there was "no supervision of the scheme" and the deaths of school children was "like murder".
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"Nitish Kumar should resign immediately as it was the responsibility of his government to supervise the implementation of the scheme," Paswan said.
He said adequate care should have been taken while cooking food for school children and teachers should have first tested the food before serving it to children.
The Rajya Sabha member said he had suggested during the HRD Ministry Consultative Committee meeting in March that there are problems in the midday meal scheme in the state and there should be proper supervision of the scheme.
On the Rs 2 lakh compensation announced by Nitish Kumar for the families of victims, he said, "it is like rubbing salt on their wounds. They must be given Rs 20 lakh to each and a government job for one member in the family."
Paswan said since the lapse has been done by the district authorities, a DIG will not be able to do a fair job.
"The inquiry must be carried out by a sitting judge of the High Court," he said.