On Saturday, police reportedly used tear gas and rubber bullets, injuring scores of the teenagers - though the authorities denied this.
Police in Bangladesh's capital fired tear gas and rubber bullets Monday to disperse hundreds of demonstrating students, while a prominent human rights group demanded the release of an activist arrested for criticizing the government during more than a week of protests. At least 12,000 people die in the country every year in road accidents that are often blamed on faulty vehicles, reckless driving and lax traffic enforcement.
Nihad El Aabedy and Raheela Mahomed report.
Bangladeshi expatriates have been thoroughly vocal about their support regarding the student protests taking place in the capital as well as the rest of the country.
"It's not true. Nothing happened at Jigatala", Dhaka police spokesman Masudur Rahman told AFP.
Non-student "saboteurs" were using school uniforms and ID cards, the Prime Minister said.
"We are deeply concerned about the reports of violence and call on all for calm", the United Nations resident coordinator Bangladesh Mia Seppo said.
Hasina's warning came as protesters marched towards the scene of Saturday's clashes chanting "We want justice!"
The trigger for the protests and the subsequent crackdown might have stemmed from demands for road safety, but the larger context is a sense of dissatisfaction with the ruling party.More news: MOVE TO IMPEACH SARAKI: In desperation, Senators move to private residence
Authorities have pleaded with demonstrators to call off protests that have almost paralysed Dhaka and prompted foreign embassies to issue travel alerts. Awami League leaders claim the party president's office was attacked by the vested quarter.
Police sources said the DMP has already collected a huge number of photos and other documents, by which they have identified the men throwing stones at police to be members of Jatiyatabadi Chhatra Dal Islami Chhatra Shibir, student members of the BNP and Jamaat-e-Islami, respectively. The government blocked 3G and 4G internet services for a period on Saturday evening - disrupting protesters' efforts to organise and share their actions.
The report adds: "AP photojournalist AM Ahad was badly beaten in the head and in his legs by Chharta League men while he was covering the students' protest in front of Dhaka City College".
But their pleas have had little effect.
An insensitive comment by Shajahan Khan, a government minister with ties to powerful transport unions, fuelled the flames last week.
Mr Khan questioned why there was such an uproar over the two Dhaka children but no reaction when 33 people were killed in an Indian bus crash the day before.
This student movement of Bangladesh could make it hard for the ruling party in the coming general elections because on Saturday the incident has given the opposition party an opportunity to question the government.
The Philippine Embassy in Dhaka is closely monitoring the situation.