Immediately after the Question Hour, Speaker Biman Banerjee took up the adjournment motion and disallowed it.
The Congress members then walked out shouting slogans demanding action against Tapas Pal, who is a two-time Trinamool Congress MP from Krishnagar.
In an insensitive comment, Pal had threatened to kill opposition CPI-M workers and have their women raped if a single ruling party worker was attacked.
Talking to reporters later, Congress Legislative Party leader Mohammad Sohrab said that "the government can file a suo motu FIR against him. We demanded a statement from the chief minister and a discussion on the issue".
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"The language used by Tapas Pal is abominable, the chief minister and other leaders of Trinamool Congress must clear their stand on this issue," senior Congress MLA Manas Bhuniya said.
"The situation demands suo motu action from the government and the party," Bhuniya, a former West Bengal Pradesh Congress Committee president, said.
Speaking to reporters outside the House, Leader of Opposition and CPI(M) MLA Surjyakanta Mishra said that "the language used by the MP is very obscene. We had sought a discussion on the issue but the Speaker did not allow."