At least five demonstrators were killed in Bangladesh on Tuesday during violent clashes between rival student groups over quotas for coveted government jobs, police said, a day after more than 400 others were injured.

Police fired tear gas and rubber bullets as university students battled with counter-protesters backing the ruling Awami League party, fighting with sticks and hurling rocks.

The violence marks an escalation in efforts to hinder a determined weekslong campaign of sit-in protests and street marches that has ignored calls by Bangladesh's prime minister and top court for students to return to class.

Three people were killed in the port city of Chittagong.

"All three had bullet injuries," Chittagong Medical College Hospital director Mohammad Taslim Uddin said, adding that "some 35 people were injured".

Rival student groups marched in several key locations around the capital Dhaka, some throwing bricks at each other, with traffic in the city of 20 million almost ground to a halt.

As the day wore on and with some key highways blocked by the protesters, the authorities deployed the paramilitary Border Guard Bangladesh (BGB) force in five major cities including Dhaka and Chittagong.

They had been tasked with controlling "the law and order situation in view of the quota protests", a BGB spokesman said.

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 heroes from the country's 1971 liberation war against Pakistan. (AFP)