She also appealed to the north eastern states not to participate in the National Population Register (NPR) exercise.
"We have also passed a resolution against National Register of Citizens (NRC) three months ago. We will pass a resolution against CAA also within three-four days," Banerjee told mediapersons.
The CPI(M)-led Left Democratic Front (LDF) government in Kerala and Congress ruled Punjab have already passed resolutions in the respective state assemblies demanding scrapping of the controversial CAA.
Referring to the NPR, Banerjee pointed out that the form has a column seeking aA birth certificates and place of birth of parents.
"But now they (central government) are saying it is not mandatory. If it's not mandatory, you withdraw. Why will it exist in the form?" he said.
"So there is an apprehension. First they have to withdraw all these clauses, all these conditions," she said.
Banerjee requested the north eastern states and their chief ministers to go through the law carefully before taking any decision about NPR.
"Because in the name of so-called NPR, there are so many conditions, related to NRC. And I will request them not to participate in this matter, because the conditions are very bad," she said.
The CAA, passed in the Parliament last month, seeks to provide Indian nationality to Hindus, Christ, Sikhs, Parsis, Jains and Buddhists fleeing persecution in Pakistan, Afghanistan and Bangladesh before December 31, 2014.
As per the Act, such communities will not be treated as illegal immigrants now and will be given Indian citizenship.
The legislation, which has come into force on January 10, has led to countrywide protests, with students coming out on the streets in thousands in almost all the states. Civil society members, anti-BJP political parties and commoners have also joined the protests.
The north-eastern states, including Assam, have been on the boil, amid fear among indigenous communities that the law could give recognition to lakhs of immigrants who came from Bangladesh over the decades.
( With inputs from IANS )