Anti-corruption campaigner Arvind Kejriwal demanded that all charges against Trivedi be dropped while Press Council of India chairperson Markandey Katju described the arrest as wrongful.
The police action was a "bit overstretched", said the Congress.
"Till the time British laws like sedition are not removed, I will stay behind bars and continue to fight against sections like 124-A (sedition) and censorship," the 24-year-old cartoonist said.
Third-year law student, Amit Katarnaware, on whose complaint the cartoonist was arrested, said he had seen Trivedi's cartoon at an Anna Hazare protest venue in December.
"It had Kasab's face on animals peeing on the Constitution, the lions of the Ashoka emblem were replaced by wolves and the Parliament was shown as a commode," he said.
The cartoons were disrespectful of the Constitution and had hurt his religious sentiments, he said.
"He was not denigrating Parliament or the national symbol but targeting those who were denigrating the Parliament or the symbol," said Kejriwal, who plans to meet Trivedi on Tuesday.
Kejriwal and his colleagues who are a part of the India Against Corruption campaign demanded that the cartoonist be released immediately.
Katju said the arrest was a "serious criminal offence" and those responsible, politicians and police officers, should be tried and arrested.
Read more:No laughing matterTrivedi's arrest sparks debate on free speechCannot target national symbols in cartoons: Government