The Congress and the Left Front members walked out of the House in protest after Speaker Biman Banerjee announced the name of Bhunia as PAC chairman.
Later, Leader of Opposition Abdul Mannan told reporters, "The Speaker's office is being used by the TMC to serve its own political interest."
The Congress said Bhunia should tender his resignation from the post of PAC chairman.
Congress chief whip Manoj Chakraborty said, "How can he (Bhunia) go against the decision of the party? He has to resign from the post of PAC chairman."
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Leader of Opposition Abdul Mannan during the day wrote to the Speaker extending their support to Left Front Legislative party leader Sujan Chakraborty for the post of PAC chairman.
Bhunia during the recess held a closed-door meeting with Chief Minister Mamata Banerjee in her chamber.
Bhunia's name was later announced as the chairman of the PAC by the Speaker, following which the Congress and the Left Front walked out of the House in protest.
The Speaker later told reporters that he had followed the convention by offering the post to the main opposition and followed the rule 255A.
Bhunia declined to make any comment when asked. He walked out of the meeting of Congress legislators called by Mannan.
Sujan Chakraborty said, "The Chief Minister is playing dirty politics to break the alliance of Congress and CPI-M.