Raising the issue during Question Hour, Trinamool leader Saugata Roy sought action against Yogesh Varshney, a leader of the Bharatiya Janata Yuva Morcha.
"A BJP youth leader has said he will give Rs 11 lakh if anyone brings Mamata Banerjee's head to him. This is condemnable," he said.
"I urge the government to take all possible action against the leader who has threatened a popular and down-to-earth Chief Minister," Roy said.
Supporting the demand, Congress leader Mallikarjun Kharge said action should be taken against the leader.
"A strong message should be given to such people," he said.
Responding, Parliamentary Affairs Minister Ananth Kumar condemned the remarks of the BJP leader.
"The statement given by the leader is completely wrong. We condemn it. Mamata Banerjee is an elected leader and she must be respected," he said.
Varshney announced the reward after the West Bengal Police acted against a rally on Hanuman Jayanti day.
A BJP youth leader has announced a bounty of Rs 11 lakh to anyone who beheads West Bengal Chief Minister Mamata Banerjee.
Yogesh Varshney of the Bharatiya Janata Yuva Morcha made the statement after police clashed with people taking part in a Hanuman Jayanti rally in West Bengal's Birbhum district.
"She stands up for Muslims. Aren't Hindus human beings? If there were some humanity, then there wouldn't be so much discrimination against the Hindus," he said after apparently seeing a video of police assaulting the rallyists to disperse them.
"There is only one thought that crossed my mind after watching that video... Whoever will cut off Mamata Banerjee's head, I will give that person Rs 11 lakh as reward," Varshney said.
Varshney's Rs 11 lakh offer has gone viral on social media, triggering outrage.
The rallyists carrying saffron flags were stopped by police and Rapid Action Force near Barabagan area, sparking trouble.
(With inputs from agencies)