The TMC, which is led by Banerjee, demanded the immediate arrest of Yogesh Varshney, a leader of the Bharatiya Janata Yuva Morcha (BJYM), while the BJP distanced itself from the controversial remark.
The Centre also roundly condemned the statement and said the West Bengal government was free to take legal action against Varshney.
"Mamata government beat up people. If someone was wearing a red shirt or a red pant, they were beaten up brutally by the police. I don't understand...Mamata Banerjee organises Iftar party, she argues for the Muslims. I want to ask her are Hindus not human?
As the Parliament roundly condemned the statement, the Centre said the West Bengal government was "free to take legal action" against him.
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Raising this issue during Zero Hour in the Upper House, TMC member Sukhendu Sekhar Roy asked the House and the government to condemn the statement, saying "a constitutionally elected CM has been described as a demon."
He said the Centre was trying to "unleash a reign of terror" in West Bengal in the name of religion and other things.
Minister of State for Parliamentary Affairs Mukhtar Abbas Naqvi said: "I strongly condemn such type of statements. The state government is free to take appropriate legal action on this issue".
BSP supremo Mayawati termed it as a "serious matter" and said "BJP should not just condemn the statement, but should also take action."
Other opposition parties including Congress, Left and SP, also supported TMC on this issue and condemned the incident.
Jaya Bachchan (SP) said there was a need to take "aggressive" steps for protection of women. "You can protect cows and women are facing atrocities," she added.
BJP member Roopa Ganguly said she too was a woman and "I was beaten up by 17 goons of TMC in front of policemen. The Chief Minister who is also a women should answer this."
In the Lok Sabha too, the BJP youth leader's bounty offer was condemned by all sides, with Parliamentary Affairs Minister Ananth Kumar saying such a statement by anyone was completely wrong and the government strongly condemns it.
Speaker Sumitra Mahajan said there have been many unpleasant incidents in the political discourse in recent past and everyone must work together to improve it. "This is completely wrong. All sides must exercise restraint."
Raising the issue soon after the House assembled to take up the day's business, TMC member Saugata Roy said "Mamata Banerjee is not only an elected Chief Minister but a former member of this House too. It is a serious and alarming behaviour and the House must condemn it. She is a grassroot leader and government must take action on it."
"A strong message should go from the government against such behaviour and action must be taken against the guilty."
TMC secretary general Partha Chatterjee said in Kolkata that the threat has been issued by "rogue element of politics" and asked why Varshney was not arrested immediately.
BJP general secretary Kailash Vijayvargiya, who is in charge of the party in West Bengal, said that he condemned such statement which propagated violence.
"We do not agree with such remarks. There is anger against Mamataji for her appeasement politics, but (we) cannot support violence. We condemn such statements."
"Such kind of statements have nothing to do with healthy politics. This is nothing but a reflection of an unstable mind," Ghosh told reporters in Kolkata.
The Congress and the Left Front also came down heavily on Varshney.
"We are against such cheap statements. Such kind of statements not only propagate violence but also create an atmosphere of polarisation. Immediate action should be taken against him," state Congress president Adhir Chowdhury said.
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Congress leader Digvijaya Singh said in the Rajya Sabha that the BJP should expel the youth wing leader who made the controversial comments against Mamata Banerjee.
Describing it is a serious issue, Singh said, "At least the Prime Minister should say on his official twitter handle that he condemns it".
Tapan Kumar Sen of CPI (M) said, "Has a new enterprise been born, to have the business of heads?... Not only in West Bengal, but in many places, for beheading, a rate is called.