She also urged students to continue the movement against the CAA and the proposed National Register for Citizens (NRC) without bowing down to threats and repression.
"In the BJP-ruled states, particularly UP, brute force is being used to curb the movement. I would like to tell the BJP, don't try to suppress the movement through use of force. If anybody tries to terrorise people, use brute force, then the people of India, of Bengal, will not support that," Banerjee said.
"They say they will take action against protestors. We also have laws. We are warning them. In many states other parties are in power. If they start doing the same against the BJP, they will be in problem," the Trinamool Congress (TMC) supremo said.
The peaceful protests would continue till the CAA was repealed, she iterated. "The agitation for protecting one's rights will continue, even if one has to give his life for that. The movement will continue till the law is scrapped," Banerjee said at Rajabazar in north Kolkata before leading yet another march, fifth, against the Act.
Criticising the BJP as one of its leaders called the protestors "goondas", Banerjee said, "Is it democracy? This is peoples' movement for democracy. This is not a movement of adangabaaz (rioters)".
If the people lost the faith in a government, it could not remain in power, she added.
Addressing a large gathering in the Muslim-dominated area, Banerjee extended full support to students fighting the CAA and the NRC.
"The students are being threatened that their careers would be finished. They have even shut students' hostels in Delhi. They are afraid of this movement.
"They (students) should not bow down to these threats and continue their protests," she said amid blowing of conch shells and beating of kasor (a metal plate that is struck with a stick to make a musical noise), and incessant slogans of "No CAB, No NRC".
Despite the Citizenship Amendment Bill becoming an Act, the TMC is still using 'CAB' in most of its posters and slogans.
The march went past Narkeldanga, Sealdah station, Acharajya Jagadish Chandra Bose Road, Nonapukur before culminating at Mullickbazar. People lined the streets to welcome Banerjee.
The CAA 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, they will not be treated as illegal immigrants and will be granted Indian citizenship.
The law has caused protests across the country claiming over 20 lives.
In Bengal, trains, buses and railways stations have been torched and damaged, and roads and train traffic blockaded by protestors.
( With inputs from IANS )