The resolution was moved by Bengal Parliamentary Affairs Minister Partha Chatterjee at a special session of the House.
The Left and the Congress members are backing the resolution, though they have expressed their dismay at the state government not allowing them to move resolution against the controversial Citizenship (Amendment) Act (CAA) earlier this month.
Congress MLA and leader of the opposition Abdul Mannan and leader of the Left Front legislature party and CPI-M lawmaker Sujon Chakraborty are present in the House.
BJP legislator Swadhin Sarkar opposed the resolution.
On January 20, Chief Minister Banerjee announced that a resolution against the Citizenship (Amendment) Act will be passed in the state assembly.
Banerjee and her Trinamool Congress have been at the forefront of the widespread protests against the legislation in the state, which also saw violence and vandalism after the law was passed last month.
The Congress and Left had earlier in the month tried to bring such a resolution in the Assembly but the Trinamool did not agree, and the matter was not included in the list of business of the House.
Since then, these opposition outfits had been ridiculing the Trinamool, describing its reluctance as another evidence of a covert alliance between Banerjee and prime minister Narendra Modi.
However, after Banerjee's announcement, Chatterjee wrote to Mannan and Chakraborty seeking their support for the resolution.
The Communist Party of India-Marxist-led Left Democratic Front (LDF) government in Kerala and Congress-ruled Punjab and Rajasthan have already passed resolutions in the respective Assemblies demanding scrapping of the controversial CAA.
Telangana Chief Minister K. Chandrashekhar Rao has also announced that the state Assembly will pass a resolution against the Act.
The CAA, passed in Parliament in December 2019, seeks to provide Indian nationality to Hindus, Christ, Sikhs, Parsis, Jains and Buddhists who fled religious persecution in Pakistan, Afghanistan and Bangladesh till December 31, 2014.
As per the Act, such communities will not be treated as illegal immigrants now and will be given Indian citizenship.
( With inputs from IANS )