Rana's comments came after three people were killed in a knife attack at a church in Nice last week.
An FIR has been registered against Urdu poet Munawwar Rana for allegedly defending the recent killings in France over a caricature of Prophet Muhammad, police said on Monday.
The case has been lodged against Rana at the Hazratganj police station in Lucknow under various Indian Penal Code sections, including 153A (promoting enmity between different groups on grounds of religion and doing acts prejudicial to maintenance of harmony), 295A (deliberate and malicious acts intended to outrage religious feelings), an officer said.
The poet has also been booked under IPC Section 505 (statements conducing public mischief) and Section 66 of the Information Technology Act, the officer said.
In a purported video clip of an interview to a news channel that went viral on social media, Rana can be heard saying, "If any person makes such a bad cartoon of my father or mother, then I will kill him."
When specifically asked if he is supporting the entire incident, he said: "I will kill him..."
Rana's comments came after three people were killed in a knife attack at a church in Nice last week. A few weeks ago, an assailant decapitated a French middle school teacher who showed caricatures of Prophet Muhammad for a class on free speech.
Police have lodged the FIR taking cognisance of the interview and a probe is on, the officer said.
WATCH: FIR against poet Munawwar Rana
