BJP's three MLAs were not present in the House during the discussion on the motion.
The West Bengal Assembly passed on Tuesday a motion against the final draft of the National Register of Citizens in Assam and adopted an unanimous proposal condemning it.
The motion was moved under the Rule 185 by state Parliamentary Affairs Minister Partha Chatterjee.
"We have to stage a protest together irrespective of our political colour. The NRC is nothing but a game plan for vote bank politics," Mr Chatterjee said.
He claimed several well-known people have expressed their wish to visit Assam in this connection.
Leader of Opposition Abdul Mannan (Congress) questioned the silence of Prime Minister Narendra Modi on the issue and said that if needed political parties might visit the national capital to stage protest against the NRC in Assam.
Senior CPI(M) leader and Left Front legislature party leader Sujan Chakraborty expressed his concern and described the entire exercise as anti-human.
The BJP's three MLAs were not present in the House during the discussion on the motion.
Mr Mannan and Mr Chakraborty had on Monday demanded that a motion be brought in the Assembly to discuss the issue.
Registrar General of India Sailesh had announced in Guwahati on Monday that 2,89,83,677 people were found to be eligible for inclusion in the final draft of the NRC out of a total 3,29,91,384 applicants and around 40.07 lakh of them did not find a place in the document.
The fate of these about 40 lakh people remains in limbo with the Centre declining to comment on their citizenship status.
West Bengal Chief Minister Mamata Banerjee today warned that exclusion of 4 million people from National Register of Citizens (NRC) in Assam could lead to "bloodbath" and a "civil war" in the country.
She also asked Union Home Minister Rajnath Singh to clarify whether the Centre intends to carry out an exercise similar to NRC-Assam in her state.
Ms Banerjee had hit out at the Centre accusing it of resorting to "vote bank politics".
"This divide and rule policy will finish the country," she told a press conference in Kolkata and alleged it was a "gameplan" to isolate and "throw out of the state" Bengali speaking people and Biharis.
Ms Banerjee also claimed that names of people who have passports, Aadhaar and voter cards have also been excluded from the final draft.
Assam, which has witnessed an influx of people from neighbouring Bangladesh since the early 20th century, is the only state to have the NRC, which was first prepared in 1951.
The current NRC is being updated with March 24, 1971 as the cut-off date to include names of genuine Indian citizens.