"If the BJP is sincere, let it put the bill to vote in Parliament or convene a joint session," she said.
Insisting it was not an "electoral issue but a matter of social justice for the party," she argued if "POTA could be passed without unanimity, why not this bill."
Rubbishing BJP's new proposal on double membership, she alleged that "these are just ways to get rid of the bill".
"It was after a long struggle that the present bill was taken up in Parliament. Any talk of changes will not be accepted," Soni said.
Delhi Chief Minister Sheila Dikshit said Congress would make the quota issue a plank during the coming assembly elections in Delhi.
Congress MP Margaret Alva challenged the BJP to put the bill to vote. "The Congress and the Left parties have all expressed support to the bill", she said, "The bill should be listed and passed in this session."
Senior Congress leaders Jayanti Natarajan and Mohsina Kidwai also addressed the rally.
Later hundreds of protesters, including All India Mahila Congress president Rita Bahuguna Joshi, courted arrest.