Bangladeshi students set fire to the country's state broadcaster on Thursday, a day after Prime Minister Sheikh Hasina appeared on the network seeking to calm escalating clashes that have killed at least 32 people.

Hundreds of protesters demanding reform of civil service hiring rules fought back and overwhelmed riot police who had fired at them with rubber bullets, chasing the retreating officers to BTV's headquarters in the capital Dhaka.

The incensed crowd then set ablaze the network's reception building and dozens of vehicles parked outside, a BTV official said on condition of anonymity.

The broadcaster said "many people" were trapped inside as the fire spread but another official from the station later said that they had safely evacuated the building.

Hasina's government has ordered schools and universities to close indefinitely as police step up efforts to bring the country's deteriorating law and order situation under control.

The premier appeared on the broadcaster on Wednesday night to condemn the "murder" of protesters and vow that those responsible will be punished regardless of their political affiliation.

But violence worsened on the streets despite her appeal for calm as police again attempted to break up demonstrations with rubber bullets and tear gas volleys.

At least 25 people were killed on Thursday in addition to seven killed earlier in the week, according to a tally of casualty figures from hospitals, with hundreds more wounded.

Police weaponry was the cause of at least two-thirds of those deaths, based on descriptions given by hospital figures.

"We've got seven dead here," said an official at Uttara Crescent Hospital in the capital Dhaka.

"The first two were students with rubber bullet injuries. The other five had gunshot injuries."

Nearly 1,000 others had been treated at the hospital for injuries sustained during clashes with police, the offical said, adding many had rubber bullet wounds.

Didar Malekin of the online news outlet Dhaka Times said that Mehedi Hasan, one of his reporters, had been killed while covering clashes in Dhaka.

Several cities across Bangladesh saw violence throughout the day as riot police marched on protesters who had begun another round of human blockades on roads and highways.

Helicopters rescued 60 police officers who were trapped on the roof of a campus building at Canadian University, the scene of some of Dhaka's fiercest clashes on Thursday, the elite Rapid Action Battalion police force said in a statement.

Near-daily marches this month have demanded an end to a quota system that reserves more than half of civil service posts for specific groups, including children of veterans from the country's 1971 liberation war against Pakistan.

Critics say the scheme benefits children of pro-government groups that back Hasina, 76, who has ruled the country since 2009 and won her fourth consecutive election in January after a vote without genuine opposition.

Her administration is accused by rights groups of capturing state institutions and stamping out dissent, including by the extrajudicial killing of opposition activists.

Mubashar Hasan, a Bangladesh expert at the University of Oslo in Norway, said the protests had grown into a wider expression of discontent with Hasina's autocratic rule.

"They are protesting against the repressive nature of the state," he said.

"Protesters are questioning Hasina's leadership, accusing her of clinging onto power by force," he added. "The students are in fact calling her a dictator."

Bangladeshis reported widespread mobile internet outages around the country on Thursday, two days after internet providers cut off access to Facebook – the protest campaign's key organising platform.

Junior telecommunications minister Zunaid Ahmed Palak said that the government had ordered the network cut off.

He earlier told reporters that social media had been "weaponised as a tool to spread rumours, lies and disinformation," forcing the government to restrict access.

Along with police crackdowns, demonstrators and students allied to the premier's ruling Awami League have also battled each other on the streets with bricks and bamboo rods.

Hasina's national address did not assign responsibility for the deaths, but descriptions from hospital authorities and students suggest at least some died when police used supposedly non-lethal weapons on demonstrations.

Rights group Amnesty International said video evidence from clashes this week showed that Bangladeshi security forces had used unlawful force. (AFP)