The Congress alleged that it was a "politically sinister motive" on the part of the government to assault opposition lawmakers to hide these companies' activities, while the Bharatiya Janata Party (BJP) also condemned the unprecedented fracas in the house, in which three legislators were injured and hospitalised.
Taking a dig at the Mamata Banerjee government, the BJP dubbed the incident as a "black episode".
The fracas broke out when the Left Front moved an adjournment motion over the state government's alleged failure to curb chit funds in the state.
After Assembly Speaker Biman Banerjee rejected the plea, lawmakers from the two sides came to blows. Following the scuffle, the house was adjourned.
"See, raising demands for a discussion on an issue in the assembly is not surely a politically motivated action. Any party can demand a discussion on any issue," said union Minister of State for Urban Development and Congress MP Deepa Dasmunshi.
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"I think to reject the demand of admitting an adjournment motion was to hide the activities of the chit funds in the state. It is a politically sinister motive from the part of the government to assault the lawmakers of the opposition in order to conceal the workings of those companies," she said.
Three Left legislators - Amjad Hussain, Nazibul Haq and Sushanta Besra - have been suspended by the speaker for the day.
BJP also condemned the incident and alleged that the government is "very intolerant".
"Assembly is not a place for fist-fighting. This is a black episode. I wondered why the government is becoming so intolerant. A discussion should have been take place in the house on chit funds. If the opposition members could not raise their voice against the government within the house, then it is a big attack to the democracy," said state BJP president Rahul Sinha.
Sinha, however, took a dig at both the Communist party of India-Marxist (CPI-M) and the Trinamool on the chit fund issue.
"I think that on chit funds, the CPI-M has no right to speak. Because, all these companies in the state had started their operations during the erstwhile Left Front government. And now these firms are gathering strength during the regime of Trinamool Congress," he said.
"Earlier, the CPI-M was run from the chit funds' money and now the Trinamool is being funded by these companies," the BJP leader alleged.
The Reserve Bank of India (RBI) has recently said that it had already warned all the state governments, including West Bengal, about the mushrooming of chit funds and also written to them to take appropriate actions against them for duping depositors.