Referring to her video address made on Friday, Swamy wrote on Twitter: "The true Nazis are the Nazi soldier's daughter led uprising on a lie that CAA is anti Muslim! If you are pro Hindu then you must be anti Muslim. If you are pro Muslim you are secular"
On Friday, Congress had attacked the Modi government for using "brute force to suppress dissent" and said that it stood by the students and protesting citizens.
In a video message, Gandhi said that the Congress expresses deep concern and anguish on the use of force against students and citizens of the country and stands in solidarity with them.
"In a democracy, people have the right to raise their voice against wrong decisions and policies of the government and register their concerns... The BJP government has shown utter disregard for people's voices and chosen to use brute force to suppress dissent.
"This is unacceptable in a democracy and the Congress condemns the use of violence and expresses solidarity. The CAA is discriminatory and the proposed NRC will target the poor and vulnerable sections of the society."
The Congress, which has not been directly involved in the protests so far with only a few leaders participating, has now come at the forefront of the agitation with it party chief expressing her support to the nation-wide agitations.
At a meeting of the party's core group on Thursday, many leaders, including General Secretary Priyanka Gandhi, had suggested that the party should support the anti-CAA agitation.
The ruling BJP, on the other hand, has long been accusing the Congress of instigating the protests but on Saturday Congress was slammed for not being seen prominently spearheading the anti-government protests.
( With inputs from IANS )