A group of BJP activists also gheraoed the official residence of the minister here and asked him to step down on moral grounds for the death of about 62 children at Sishu Bhavan.
"This is high time, the minister steps down and the government ensures that no more children dies at Sishu Bhavan," BJP leader Samir Mohanty said.
Party leader Nayan Mohanty led the agitation in Cuttack.
BJP's Kendrapara district unit accused the health minister of "inefficiency" leading to the death of the children at Sishu Bhavan.
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The party alleged that infant deaths are not taking place alone at Sishu Bhavan in Cuttack, but also across the state.
Expressing concern over the deaths, Odisha Pradesh Mahila Congress Committee today announced its plan to organise a march to 'Naveen Niwas', the residence of chief minister Naveen Patnaik tomorrow.
Meanwhile, health and family welfare Nayak said, "the BJP's agitation is politically motivated. A senior BJP leader who lost elections against me in 2014 polls, has been engineering such agitation. There should be no politics over the death of children.