The students are arguing that the system is discriminatory, asking for recruitment based on merit.
The government has been trying to quell the protests, on Thursday switching off the country’s mobile internet in an attempt to slow the students.
Instead, it became the deadliest day so far, according to news agency AFP. According to its count citing hospitals, a total of 32 people have died during the protests.
The BBC’s Bengali service has confirmed 19 deaths so far – 13 of them on Thursday. Among the dead was a 32-year-old journalist for the Dhaka Times.
Sheikh Hasina had condemned protesters’ deaths as “murder” in her Wednesday television appearance, but her words were largely dismissed by protest organizers, who rejected government offers of talks.
“The government has killed so many people in a day that we cannot join any discussions in the current circumstances,” said Nahid Iqbal, a leader of the anti-quota protest.
Another student, Aleem Khan, 22, told the BBC: “The Prime Minister is asking for an end to the violence with one hand whilst, with the other hand, attacking students using pro-ruling party groups and the police.”
Thursday saw tear gas and rubber bullets deployed by officers, as students created human blockades in the streets.
The students who stormed BTV had earlier “torched” a police station, according to an official at the network.
“They chased the police officers when they took refuge at the BTV office,” the official told AFP. “Angry protesters then caused mayhem here.”
Elsewhere, BBC Bengali spoke to a group of medical students who were taking shelter inside a medical college compound after they were attacked by pro-ruling party groups.
One of the students, Sumi, told the BBC: “I am here to protest against discrimination within the civil service and now that so many students have been killed by the police, I am also protesting against that.
“Our protest is peaceful, but the way in which we were attacked made me feel like we were going to be killed by pro-ruling party groups.”