Modi, who earlier in the day attended the centenary celebrations of the varsity here along with Kumar, said measures like grant of central status were a thing of the past.
The prime minister said his government has taken "a step forward" towards making 10 private universities and 10 government ones world-class.
"Both of them (Modi as well as Kumar) are making fools of people of Bihar. They must have decided beforehand that one will propose and another would dispose it (proposal for central status to PU)," Prasad told reporters at Patna's Jay Prakash Narayan Airport on his arrival from New Delhi.
The RJD chief has been on the offensive after the disintegration of the grand alliance government in Bihar in which his son Tejaswi Yadav was deputy chief minister.
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During the fucntion, Modi said the Centre will provide assistance of Rs 10,000 crore to 10 private universities and as many government ones for a period of five years.
"I exhort Patna University to seize this opportunity," he added.
Prasad, taking a swipe at Modi, said, "Will he (PM) be on the chair till that time?"
The RJD chief also questioned BJP president Amit Shah for giving a "clean chit" to his son Jay Amit Shah, whose company saw a huge rise in turnover after the BJP came to power in 2014, as claimed in a report by The Wire.
"Are you (Amit Shah) heading ED or CBI that you are giving clean chit to your son Jay Shah?" he said.