Posters at the protest site in south-east Delhi and also circulating on social media platforms read: "PM Modi, please come to Shaheen Bagh, collect your gift and talk to us."
"Whether Prime Minister Modi or Home Minister Amit Shah or anyone else, they can come and talk to us. If they can convince us that whatever is happening is not against the Constitution, we will end this protest," said Syed Taseer Ahmed, one of the first protesters at Shaheen Bagh.
He said according to the government's claims, the CAA was "to award citizenship and not to take away someone's citizenship", but nobody explained "how is it going to help the country".
"How is the CAA going to help us tackle issues of unemployment, poverty and economic slowdown, which are the most pressing issues," Ahmed said.
Protests against the CAA and the NRC unfolded at Shaheen Bagh, Zakir Nagar, Jamia Nagar, Khureji Khas and other places in Delhi and elsewhere in the country in December.
The Shaheen Bagh protesters have pitched a tent on a main road linking Noida to southeast Delhi via the Kalindi Kunj bridge, which, according to an official estimate, witnesses movement of around 1.75 lakh vehicles on a daily basis.
Ahmed said school buses, ambulances and emergency vehicles were allowed hassle-free movement since the protest started and the claim that the stir was causing a lot of problems to the common people was "exaggerated".
"Had it been at the levels as it is being portrayed by some people, we would have been evacuated from here long ago. The BJP would have won the Delhi polls and the Centre would have removed us. So, this claim that the Shaheen Bagh protest is causing major inconvenience is unsubstantiated," he added.
According to the CAA, members of Hindu, Sikh, Buddhist, Jain, Parsi and Christian communities who have come to the country from Pakistan, Bangladesh and Afghanistan till December 31, 2014, after being subjected to religious persecution will not be treated as illegal immigrants but given Indian citizenship. The law excludes Muslims.
Those opposing the law contend that it discriminates on the basis of religion and violates the Constitution. They also allege the CAA, along with the NRC, is intended to target the Muslim community in India.
However, the Centre has dismissed the allegations, maintaining that the law is intended to give citizenship to persecuted people from the three neighbouring countries and not to take away the citizenship of anyone.