Led by Chief Minister Kamal Nath, the march covered a distance of about two kilometres from Roshanpura square to Minto Hall.
The state is one of the few non-BJP-ruled state that have refused to enforce the new CAA, which was passed by Parliament winter session.
Criticising the Bharatiya Janata Party, Kamal Nath said that the BJP at the Centre has been raising issues and bringing up such legislature that would divert public attention from its failure on the administrative front.
"The peace march that we have taken out is not just for Bhopal or the state, it is for the nation. We want to send this message from the heart of the country on how the central government is trying to disintegrate the country.
"The question is not about what is written in these laws. The question is about what the government is trying to hide about them. The question is not what they will be used for. The question is about how these laws will be misused," Kamal Nath said.
"The Union Home Minister has said in Parliament that the NRC will be enforced in the entire country. Any law which is anti-Constitution, anti-national, anti-religion will not be enforced in Madhya Pradesh.
"The NRC and CAA have hidden political intents of the BJP. We have to protect the Constitution and culture of the country," the Chief Minister said.
A large number of activists from diverse organisations and people from all walks of life and the state ministers took part in the march.
The march started from the busy Rangmahal intersection and covered the two km distance to the old Vidhan Sabha building, Minto Hall in over an hour. Some other Congress leaders who spoke before the start of the march said the party had to hit the streets to protect democracy.
The Congress leaders who were enthused by the response to the march said "it was not just their workers who had taken to the streets on the issue. All those who opposed the unfair law that threatens the unity of the nation were represented in the march.
"It is the people from diverse ideologies who have shown solidarity for democracy and unity of the country".
The BJP reacted sharply to the Congress rally. Former Chief Minister Shivraj Singh Chouhan said the Congress was misleading the people and supporting divisive forces.
( With inputs from IANS )