However, hospital staff said dozens of people had been injured, some seriously.
For those unversed, two students of Dhaka's Shaheed Ramiz Uddin Cantonment College were killed when a speeding bus ploughed through a crowd on July 29.
As the protests grew in recent days, students stopped vehicles - including those belonging to government officials - to ask them for their papers and licences.
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.
Witnesses said police fired rubber bullets and tear gas at demonstrators and that alleged pro-government activists attacked youngsters, including some of those rushing to nearby hospitals for treatment.
The BCL were also blamed for attacks on journalists - including the destruction of phones and cameras - which the Daily Star newspaper called a "reprehensible violation" of press freedom.
A Bangladeshi child holds a placard, as she participates with protesting students in Dhaka.More news: Ruby Rose to Play Batwoman for The CW
A photographer for an worldwide news organisation was among those beaten.
Earlier, the US Embassy expressed its support to the protesters by saying that "nothing can justify the brutal attacks and violence over the weekend against the thousands of young people, who have been peacefully exercising their democratic rights in supporting a safer Bangladesh".
The Bangladesh Telecommunications Regulatory Commission said it would comment later Sunday.
"We must bring changes", said Selina Akter, a mother of two schoolchildren who joined the group.
Detectives also detained award winning photographer Shahidul Alam, founder of Drik Picture Library, last night for interrogation over his Facebook posts on the ongoing student protest.
Road accidents kill 12,000 people and cause 35,000 injuries in Bangladesh each year, says the Accident Research Institute of state-run Bangladesh University of Engineering and Technology.
The government blocked 3G and 4G internet services for 24 hours on Saturday evening in response to the protests, with young people complaining that this is to stop them organising and sharing their actions.
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.
He said the party office which was close to Jigatala was vandalised by some unidentified youths, dressed in school uniforms, moments before the clashes erupted.