The saffron party leaders held a dharna near BJP state headquarters here, when Patnaik was addressing school students on the occasion of Children's Day.
The party also criticised Patnaik's mode of addressing children earlier in the day.
"The chief minister used a teleprompter to address the students in Odia language. If he (Patnaik) reads out a 20-page Odia language book in front of the media, we will give a cash prize of Rs 1 lakh to Patnaik," an official statement released by the state BJP, said.
Taking a jibe at him, BJP vice-president Sameer Mohanty said, "How could Naveen Patnaik suddenly develop love for children after 17 years of rule? The hidden reason is publicity using public money."
Mohanty further alleged that the state government spent about Rs 200 crore from the state exchequer for Children's Day celebrations.
The ruling BJD, however, rejected the allegations made by the Opposition party.
"If the CM wants to give students a message on Children's Day, the BJP should be happy. Why it is getting so intolerant?" Dash wondered.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)