Some of protesters broke barricades and clashed with police when they were stopped from going towards Swamy's residence.
The protest was led Delhi Congress leaders Haroon Yusuf and Mukesh Sharma.
"Swamy's allegations are totally baseless. We condemn his derogatory remarks and demand an unconditional apology immediately failing which we will intensify our protest. We would gherao wherever he goes, be it railway station, airport, bus stand or any other public place," Yusuf said.
"This is not at all acceptable. He must apologise for the baseless allegations and vitriolic attacks," said Sharma, Chief Spokesperson of DPCC.
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As hundreds of Congress workers, carrying placards and flags reached the gate of society where Subramanian Swamy resides, police closed the entry points following which the protesters clashed with them.
Police had put barricades at about 50 metres from Swamy's house. Police dispersed the agitators using mild force.
"Today, all Congressmen came out on street to show their resentment against Swamy's comments. We would not tolerate such statements," Yusuf said.