The ensuing confrontation was violent. And bloody.
Country's direction at stake
What is happening in Bangladesh is a push and pull between two forces to determine the future direction of the country.
In February, thousands and thousands of youths held a month-long sit-in in another part of the capital, Shahbag, demanding the death penalty for those who took part in war crimes during Bangladesh's bloody battle for independence from Pakistan.
Many of those accused of war crimes now hold prominent position in Islamist parties.
The rallies, led by youths and fueled by social media, also tried to achieve something else: a ban on extreme fundamentalist parties.
But Bangladesh is also the fourth most populous Muslim country in the world.
And the radical elements of the religion were not going to sit by idly as those rallies grew.
The Islamists let their presence known with larger and larger rallies and strikes, first in cities outside Dhaka and then in the capital city.
Each time they came out, police officers with batons followed.
Clashes ensued. Properties were destroyed. Lives were lost.
The Islamists' tactic has been to turn the criticism on its head: By criticizing them, they seemed to say, you criticize Islam.
They called the Shahbag participants "anti-Islamic atheists" who deserve death for defaming the religion but who are protected by the government.
And so, when the Hefazat-e-Islami protesters gathered Sunday, that was one of their main demands: put to death these "atheists."
Battles for hours
Clashes broke out when Hefazat activists tried to break a police cordon.
The street battles went on for hours, with police firing rubber bullets and tear gas and the Islamists hurling crude explosives and chunks of brick.
Syed Ashraful Islam, secretary-general of the ruling Awami League and a government minister, said demonstrators set fire to the Communist Party of Bangladesh office and ransacked several other business establishments in central Dhaka.
Shahriar Shahid, the managing editor of BSS, said the service had to suspend operations for the day after Hefazat activists set a fire at the entrance of its office.
Blame to go around
The government, rights groups say, shares blame not just for its crackdown but also for muffling the free speech of the Islamists.
On Monday, authorities shut down the offices of pro-Islamist Diganta Television and Islami TV stations after they aired footage of the clashes.
"They came in early in the morning and ordered us closed," staffer Tanvir Hussain told CNN.
Information Minister Hasanul Haq Inu told reporters the stations "provoked violence (by) spreading hatred and rumors."
Last month, the government shut down another opposition newspaper.