Banerjee appealed to all parties except the BJP to build up a "people's movement" against the law across the country, and accused the BJP-led NDA government at the Centre of playing a "communal game" on the issue.
"I have congratulated all parties who have taken a stand... Let us all build a people's movement across India with all our strength," she told newspersons in Digha of East Midnapore district.
Expressing satisfaction over Punjab Chief Minister Amarinder Singh and his Kerala counterpart Pinarayi Vijayan announcing they won't implement CAB or NRC in their state, she appealed to both states to build up a mass movement.
"They can jail us, they can torture us. We are prepared to withstand that. But we will never accept CAB and NRC and allow them (BJP) to divide the country," she said.
Banerjee said her party had earlier tried to reason with the Central government not to go ahead with CAB as the various sentiments of particular states needed to be respected.
"But they said they would implement it forcibly," she said.
In the backdrop of intense protests in the Northeast, Banerjee said: "There is unrest throughout the nation. Dark clouds are hovering."
She said "Assam is burning", and alleged that atrocities were being committed on the people.
"I don't want violence to increase. But I want people to protest democratically. One has to protest. If they (BJP) think they can repeat the strategy they employed in Kashmir to gag people by imprisoning political leaders for months, (they should know) it doesn't happen that way," she said.
Banerjee said she felt 'bad' at the postponement of Japanese Prime Minister Shinzo Abe's visit to India.
"Doesn't it lower our prestige? India is our pride. We are proud to say we are Ind," she said.
Japan is the second nation to postpone visit, as Bangladesh's Foreign and Home Ministers have also cancelled their trips to India, .
Banerjee also refered to the alleged attack on the convoy of the Bangladesh assistant high commissioner (AHC) to Guwahati and vandaliaation of signposts.
"What turn has our relations with Bangladesh taken? Since the 1971 Bangladesh Liberation War, we have had a good relation with them. Whenever they come to our country, the first thing they always do is praise the Indian government and the people. And we never call (Bangladesh Prime Minister) Sheikh Hasina communal. She is Bangabandhu's (Sheikh Mujibur Rahman - the first president of independent Bangladesh) daughter.
"Even these people are tense, they are cancelling their programmes. Bangladeshi convoy has been attacked. This has never happened in the past. You need to love the country, and take everybody along," she said.
( With inputs from IANS )