A group of students from Dhaka National College gathered at Rampura Bridge around 9:45 am on Tuesday. Students from Cambrian College and Banasree Ideal School and College also joined them.
Traffic came to a halt when protesters blocked DIT road, said Rafiqul Islam, chief of Rampura Police Station.
The protesters chanted slogans -- 'We Want Justice' -- and carried placards that stated their demands.
Another group of student protesters staged a demonstration near the Allah Karim Mosque in Mohammadpur around 11 am, leading to congestion in the area and a halt in traffic on several routes nearby.
"Students from Mohammadpur Government College have taken to the streets with a number of demands. We're trying to calm them,” said Inspector Dulal Khan of Mohammadpur Police Station.
Students are demanding a 50 percent student discount for bus fares after authorities hiked rates following an increase in fuel price.
The death of Notre Dame College student Nayeem Hasan, who was killed in an accident with a city corporation garbage truck on Nov 24, added further fuel to the protests.
Mohammad Mainuddin, an SSC candidate from Ekramunnesa School, was run over by a bus operated by Green Anabil Paribahan on DIT Road around 10 pm on Monday. The bus was allegedly racing another.
His death further ignited tensions, with an angry mob setting fire to at least eight buses and vandalising several others.
Only a few buses were operating on the route from Motijheel to Pragati Sarani through Malibagh and DIT Road on Tuesday, the day after the incident.
Commuters were waiting for buses at different intersections in the city.
Meanwhile, the Rapid Action Battalion (RAB) has arrested Chan Mia, the helper on the bus that ran over Mainul Islam.RAB arrested Chan Mia from Sayedabad on Tuesday, said Imran Khan, assistant director at RAB Headquarters.