Priyanka Gandhi Vadra, who held the fort for the party over the last week at India Gate and met victims' relatives in Uttar Pradesh, was also present among senior party leaders Ghulam Nabi Azad, Ahmed Patel, Mallikarjun Kharge, Anand Sharma and A.K. Antony.
Madhya Pradesh Chief Minister Kamal Nath, his Rajasthan counterpart Ashok Gehlot, besides general secretaries Mukul Wasnik and K.C. Venugopal also arrived at the historic site for the protest.
Sonia Gandhi, Manmohan Singh and Rahul Gandhi read the Preamble of the Constitution to begin the Satyagrah movement in solidarity with the students and youths who have been protesting the new legislation across the country since it was passed on December 13.
The party members also observed one-minute silence in support of their cause and against the BJP-led government's policies.
Sonia Gandhi and Manmohan Singh, however, left after about an hour.
Priyanka Gandhi, before reading out the Preamble in Hindi, said in the names of all those "martyred" during the anti-CAA protests, her party resolved to protect the Constitution.
"In the name of Bijnor's 22-year-old Anas, who used to earn money for his family through a coffee-vending machine and had recently got married... In the name of 21-year-old Suleiman, who was studying for the UPSC exam and used to take tuition...," she said.
On Sunday, Suleiman's mother told her with tears in her eyes that her son was "martyred" for his country, Priyanka added.
"In the names of all the children who have been martyred in this movement... In the name of Bijnor's Omraj Saini, whose five children are waiting for him and he is in the hospital, injured... In their names, we resolve today that we will protect the Constitution and will not allow it to be destroyed," said Priyanka Gandhi, who is also party in-charge for eastern Uttar Pradesh.
Venugopal said the protest meant to oppose the "authoritarian government" and stand in support of the agitating students and civil society groups. The protest also sought to remind the government about the strength of India's Constitution.
The party has also asked its state units to organise peace marches across the states.
Mahatma Gandhi, too, had launched a similar opposition to fight against the dictatorial policies of the British rulers, the speakers said, adding the Congress has now pitched in to save Babasaheb Bhimrao Ambedkar's Constitution.
( With inputs from IANS )