The party, however, tried to deflect criticism by targeting Modi government on its stand in the court on the provision which allows arrest of a person for posting allegedly offensive content on websites.
Congress leader P Chidambaram welcomed the Supreme Court judgement holding Section 66A of the IT Act as unconstitutional.
"I welcome the judgement of the Supreme Court holding that Section 66A of the IT Act is unconstitutional.
The former Union Minister, who held the Home and Finance portfolios in UPA government, said there could be a case of misuse of freedom of speech and in such cases ordinary laws should apply and the offender should be dealt with under them.
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"If some provisions of the law have to be strengthened, that could be considered. But Section 66A was not the answer," Chidambaram said.
Party spokesperson Sanjay Jha questioned why the Modi government had "stoutly defended continuity" of the provision in the apex court when Narendra Modi had once openly opposed the provision before becoming Prime Minister.
In another tweet, he said,"Narendra Modi turned his DP (display picture) black to protest against #Sec66A . Then he did his classic U-turn to argue for it in Supreme Court as PM."
Party MP from Kerala Shashi Tharoor tweeted "Glad the Supreme Court has struck down Section 66A of the IT Act, which was liable to misuse (&has been abused). Freedom must not be curbed."
Terming liberty of thought and expression as "cardinal", a bench of justices J Chelameswar and R F Nariman said, "The public's right to know is directly affected by section 66A of the Information Technology Act."
The bench also rejected the assurance given by NDA government during the hearing that certain procedures may be laid down to ensure that the law in question is not abused.
The government had also said that it will not misuse the provision.
"Governments come and go but section 66A will remain forever," the bench said, adding the present government cannot give an undertaking about its successor that they will not abuse the same.