"BS Yediyurappa has asked the people who belong to Lingayat and Veerashaiva communities to vote for the BJP. This is a serious offence under Section 125 and 153 of the Representation of the People Act, 1951," he said.
"We will file a case against BSY and Law Minister Madhu Swamy for the violation of Model Code of Conduct," the Congress leader added.
"Why should they make candidates withdraw their nomination? BSY's son himself discussed with the candidate of Hirekerur and managed him to take back his nomination," alleged Rao.
He also alleged the BJP was trying to poach Congress MLAs in the state.
"I am giving you a warning. If you (BJP) again start Operation Kamala, the people of the state will teach you a good lesson. They have approached many of our MLAs already," he said.
By-poll to 15 assembly seats in Karnataka is scheduled to be held on December 5 from 7 am to 6 pm. The by-election will take place in Athani, Kagwad, Gokak, Yellapura, KR Pura, Yashwanthapura, Hirekerur, Ranebennur, Vijayanagara, Chikkaballapura, Hoskote, Mahalakshmi Layout, Shivajinagar, KR Pete, and Hunsu.
The counting of votes would take place on December 9.
On Monday, Janata Dal-Secular filed a complaint with the Election Commission of India against the Chief Minister for allegedly urging people to vote only for the Lingayat candidate.