Security forces have detained several people, including five university teachers suspected of instigating the protests.
Authorities also shut all universities and colleges in Dhaka and five other cities indefinitely.
The interior ministry on Monday urged citizens to be alert against any recurrence of violence and to help the government prepare for a free and fair election late next year.
Bangladesh has been under a state of emergency since the interim authority took over on January 11 following weeks of political violence that killed at least 25 people.
The government accused students and some teachers backed by political parties of trying to "destabilise the country and undermine the administration" through last week's unrest.
The government also planned to take legal action against those found responsible for fomenting "instability and chaos," the statement said.
Demonstrations, strikes, political activities or open criticism of the government are not allowed under emergency rule.
A retired high court judge would launch an inquiry into the violence from Tuesday, the United News of Bangladesh news agency said.
More than 144 people have been arrested for violating the curfew.