The Congress activists shouted slogans and displayed posters saying "No NRC, No CAA" and cried "Shame, Shame".
They marched from the Tipu Sultan Mosque in Dharmatala area to Ram Mandir on Central Avenue as part of the party's "save the Constitution, save the country" political programme.
They carried on their shoulders a symbolic corpse of the Constitution of India as a protest against the BJP government at the Centre.
"The BJP led central government is ushering in all sorts of negative politics in the country. Torching buses and trains is no solution. Similarly, we condemn the shameless baton charge on Jamia Millia Islamia University students. We also condemn the black Act," said Congress leader Ashutosh Chatterjee.
Emphasising that the culture of West Bengal was a story of co-existence of Hindus and Muslims, Chatterjee said "Congress since independence is fighting by the side of the people".
Chatterjee said the Modi government is bringing forth one issue after another to deflect the people's attention from the collapse of the economy.
"People don't have food, jobs. The entire economy has collapsed. The present central dispensation should resign," said Chatterjee.
Earlier, state Congress spokesman Amitabha Chakraborty said the state administration has refused to give permission for the rally.
"The communal BJP always gets the green signal to hold meetings and processions, but when the Congress wanted to hold a Satyagraha movement, inspired by the ideals of Mahatma Gandhi, the government refused to give the nod.
"We will begin our procession at 3 p.m. from the Tipu Sultan Mosque irrespective of whether the government gives us permission or not," Chakraborty had said.
( With inputs from IANS )