Protesters including a number of eminent citizens and leaders and activists of left-leaning political organisations have threatened to surround the Prime Minister's Office (PMO) if the Digital Security Act is not repealed by 26 March.
They have also demanded that all those arrested under the Act be released.
The announcement was made from a procession brought out demanding justice for writer Mushtaq Ahmed's death in jail custody and abolition of the Digital Security Act on Wednesday.
The demonstration started in front of the National Press Club and headed towards the PMO, but it ended in a peaceful manner in front of the InterContinental hotel at Shahbagh after being obstructed by the police at different places.
Earlier, civil society members held a rally in front of the National Press Club.
Speakers at the rally said they demand immediate revocation of the Digital Security Act.
Gonoforum President Dr Kamal Hossain and Dhaka University Professor Emeritus Serajul Islam Choudhury also expressed their solidarity with protesters however they were not present there.
In written statements read out at the rally, both of them asked for major changes to the controversial law.
Dr Zafrullah Chowdhury, founder of Gonoshashthaya Kendra; Mahmudur Rahman Manna, convener of Nagorik Oikya; Badiul Alam Majumder, Secretary of 'Sushashoner Janya Nagorik' (Sujan); Photographer Shahidul Alam; Professor Rehnuma Ahmed; journalist Faruk Wasif; Saiful Haque, general secretary of the Revolutionary Workers Party; Junaid Saki, leader of Ganosamhati Andolon; Syeda Rizwana Hasan, chief executive of Bangladesh Environmental Lawyers Association (Bela), Nurul Haque Nur, former vice president of the Dhaka University Central Students' Union (Ducsu), among others, attended the rally.
After the rally, around 200 demonstrators started to march towards the PMO around 11.15am.
The protesters marched by the High Court to Shahbagh intersection, although law enforcers obstructed the procession in front of the High Court, and at Matshya Bhaban and Sahbagh intersections.
The procession faced a police barricade near InterContinental hotel at around 2pm. After talking to police officials, the demonstrators held a brief rally there and announced the end of their march towards the PMO.
"We will not break the police barricade," said the demonstrators. Moreover, they gave roses to policemen in the area as police did not attack them.
Sazzadur Rahman, deputy commissioner of the Ramna zone of the Dhaka Metropolitan Police, said, "We thank the protesters for ending the rally peacefully. We have also been tolerant of them."
Dr Zafrullah Chowdhury said, "We will continue our movement against the Digital Security Act. I will ask the government to uphold peoples' right to speak."
Court rejects bail plea of 7 students in assaulting police
Meanwhile, the court has rejected the bail plea of seven accused in a case filed over alleged assault on police from a torch procession of progressive student organisations in the capital's Shahbagh area on Friday.
On Wednesday, Dhaka Metropolitan Magistrate Abu Saeed's court rejected their bail application after a hearing.
Meanwhile, nine leftist student organisations staged a torch procession on Wednesday evening demanding the release of the detained leaders and activists. The procession started from the Teacher-Student Centre (TSC) of Dhaka University, passed through Shahbagh and ended at the TSC.
Six BNP, Chhatra Dal leaders granted anticipatory bail
The High Court on Wednesday granted anticipatory bail to six people, including Habib Un Nabi Khan Sohail, joint secretary general of the BNP, and Sultan Salauddin Tuku, general secretary of Juba Dal, in a case of filed over clashes with police in front of the National Press Club during a student rally held on Sunday in protest of the death of writer Mushtaq Ahmed in jail.
The High Court bench of Justice Riaz Uddin Khan granted the bail.