Irrigation Minister Devineni Umamaheswara Rao on Saturday said the poll panel should take suo motu note of Mr Reddy's comments made at an election meeting in Nandyal assembly constituency, where by-polls are scheduled to be held on August 23.
He told reporters here that calling for shooting a person and that too, at a public meeting is a cognisable offence both under Indian Penal Code and Representation of People's Act.
Mr Rao claimed that whoever makes such a comment during election campaign may be jailed for three years.
He also wanted the Leader of Opposition to apologise to the Chief Minister.
The TDP leader alleged that Mr Reddy was inciting violence and said he had no right to continue as the Leader of Opposition. He said the YSRCP leader has displayed his "criminal mindset" by making this comment.
The Minister said the irresponsible remark shows that Mr Reddy was fearing defeat in the upcoming by-election.
A local leader of TDP has filed a police case against Mr Reddy, accusing him of inciting violence on the basis of caste, creed, race, religion, community or language, under the Representation of People's Act.
Mr Reddy also called Mr Naidu a "thief" while referring to the 19 MLAs, who won assembly elections as YSR Congress candidates, but switched loyalties to the ruling TDP.
The by-election in Nandyal is necessitated by the death of the sitting legislator Bhuma Nagi Reddy, one of those who defected to the TDP. His daughter Akhila Priya, who too won as a YSR Congress candidate from Allagadda constituency in the same district, is now a Cabinet Minister.
The TDP has fielded Akhil Priya's counsin Bhuma Brahmananda Reddy. YSR Congress candidate is Silpa Mohan Reddy, who quit TDP to join the opposition party after he was denied ticket.
Both the parties have made the by-election a prestige issue as it is being seen as a referendum on the three year rule of the TDP. It is also expected to indicate which way the wind was blowing in the run-up to the 2019 elections.