Several students have been injured in clashes with the police ever since the protests began, according to several media reports.
Transport workers, who went on a virtual shutdown citing security reasons for the past eight days took to the street and clashed with protestors, prompting police to use batons and tear gas canisters.
And on Monday, Bangladesh police said they arrested a prize-winning photographer Shahidul Alam for "provocative comments" in an Al Jazeera interview about the protests, seen by some as a free-speech crackdown. "The situation is chaotic".
The protests spreading across Bangladesh have highlighted traffic risks in the densely populated country, where more than 4,000 people die in road accidents each year, one of the world's highest rates, the World Bank says. The 17-year-old student, Ridwanul Islam, said, "We want justice after the accident".
The report claimed that at least 150 people - including students, pedestrians, journalists and ruling party activists - were wounded in the unrest.
"It's not true. Nothing happened at Jigatola", Dhaka police spokesman Masudur Rahman told Agence France-Presse (AFP). Bangladeshi Home Minister Asaduzzaman Khan warned on Sunday that actions would be taken against the demonstrators if the protests become too disruptive.
Ambassador Marcia Bernicat and her security team managed to leave the area unharmed, the statement said, adding that two security vehicles were damaged.
At a separate event in Banani on Sunday, Awami League General Secretary and Road Transport and Bridges Minister Obaidul Quader said: "If someone attacks the Awami League president's office, what should we do?"
The unprecedented numbers on the streets have forced the Awami League government - unable to control the protests in a week - to come to the dialogue table.
The country's biggest-circulation newspaper Prothom Alo said 3G and 4G Internet services had been shut down for 24 hours since late Saturday, shortly after the violence broke out.
Bangladesh's transport sector is widely seen as corrupt, unregulated and unsafe.
Bangladesh's transport sector is widely seen as corrupt, unregulated and risky, and as news of the teenagers' deaths became a catalyst for public anger after spreading rapidly on social media.
Prime Minister Sheikh Hasina called on students to return home and call off the protests.
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.
Meanwhile, on Saturday, an official auto carrying the USA ambassador to Bangladesh, Marcia Bernicat, was attacked by a group of armed men, some riding motorcycles, as it drove through Dhaka, according to a Sunday statement from the embassy.