Mamata Banerjee had reached out to the opposition Congress and the CPI(M) to take on the BJP.
Adhir Ranjan Chowdhury, the Leader of the Congress in the Lok Sabha, attributed the BJP's growth in West Bengal to Mamata Banerjee's "failures", raising questions on the Chief Minister's "seriousness" in her fight against the BJP in her state.
Ms Banerjee had on Thursday reached out to the opposition Congress and the CPI(M) to take on the BJP that successfully made in-roads in Bengal in the national election.
"People say something and then go back on their words. It's her nature. If she is serious (about fighting the BJP), she'll have to talk to our senior leadership. The way the BJP is growing in Bengal, it is due to Mamataji's failures," Mr Chowdhary told news agency ANI.
Speaking during the debate on the Governor's address in the state assembly, Ms Banerjee said the BJP is trying to run a parallel government in West Bengal and parties like the Congress and the CPI(M) should join hands with her Trinamool Congress to fight it.
"The people of the state are witnessing in Bhatpara what happens if you vote for the BJP. I feel all of us (TMC, Congress and CPI-M) should come together in the fight against the BJP. It doesn't mean we have to join hands politically. But on common issues at the state and the national levels, we can come together," she said.
Adhir Ranjan Chowdhury, who is a strong detractor of Ms Banerjee, was called a "fighter" by Prime Minister Narendra Modi after the all-party meeting recently.
The Congress leader, who has been representing Berhampore in West Bengal since 1999, retained the seat in this year's election.
The BJP has made deep inroads in West Bengal in the recent Lok Sabha election, winning 18 out of 42 seats. Ms Banerjee's party's seat tally fell to 22 seats, 11 down from number in the 2014 polls.
(With inputs from ANI and PTI)