"We demand that steps be taken immediately to make the statement of the law minister legally effective," the council said.
During a recent interview with BBC, Law Minister Anisul Haque said the DSA would be reviewed. The minister also said, "No arrest will be made under the DSA without an investigation."
"The journalists and people expressing free opinions are being regularly harassed and tortured because of DSA," the council said in a statement.
Also read: Kamal demands abolition of DSA
Although the physically ill cartoonist Kishore got bail after 10 months of incarceration and was released from jail in the same case, he still has to continue with the case, the council said.
"Journalist Kajol went missing and had to stay behind bars for a long time just for sharing an article on social media. Although he was granted bail, the case against a mentally, financially and the physically-affected person is ongoing," the statement read.
The council pointed out that demands had been made earlier to scrap certain sections of the act even before it was passed into law. "In September 2018, we explained our positions about the objectionable sections of the DSA and demanded cancellation of those sections. If our demands were considered, we would not have to face the situation that we are in now."
Also read: DSA protests: March to PMO stopped outside Sakura
"We raised our concern about sections 8, 21, 25, 28, 29, 31, 32, 43, and 53 of the DSA," the council said.
The DSA is ambiguous and the language of the law can easily be misinterpreted and used against the journalists, the council said.
The statement also noted the proliferation of non-bailable offences in the act, with 14 such offences listed out of 20. This all has created an atmosphere of fear in which the normal practice of journalism has become laden with risk.
Also read: Cartoonist Kishore released from Kashimpur
"We demand the immediate release of all those arrested and thrown behind bars under the DSA and the withdrawal of all cases," the statement said.
The council, however, said that a law is needed to cover criminal activity in the digital space, but that should not be allowed to curtail freedom of expression, saying, "Those who commit criminal acts on digital platforms must be brought to justice, but the law should not be applied to suppress the media and free-spirited writers."