"You can wage anti-government agitation. But make sure people are not killed and children's education is not hampered by your movement," she said after the announcement of primary school certificate and Ebtedayee exams results, reported bdnews24.com.
Hasina added there was no ban on anti-government protests, but it would be unfortunate if the purpose behind the protests was to kill people.
"Let the Bangladesh Nationalist Party-Jamaat-e-Islami agitate. But why (do they agitate) against the people? Killing people is no movement," she added.
The prime minister alleged that the opposition was hiring people at 500-2000 takas to get people killed.
Hasina said she had appealed to the opposition not to call any shutdown during public examinations but Zia was adamant.
She said if her Awami League government came to power again it would make computer education compulsory at the primary level.
Education Minister Nurul Islam Nahid said the students had to take exams amid uncertainty and violence.
Zia Sunday announced that the opposition's march to Dhaka, protesting the holding of the next general elections under the ruling government would continue Monday.
The opposition's "March for Democracy" triggered widespread violence in parts of the capital, leaving two people dead and dozens injured.
Zia got in her car to attend the march in front of her party's headquarters in Dhaka's downtown Naya Paltan area but was barred from leaving her house, where she has remained virtually confined since the announcement of the protest programme earlier in the week.
The BNP and its 17 allies, including the Bangladesh Jamaat-e-Islami, have asked Hasina to allow installation of a non-party caretaker system, or else the opposition would not participate in the next general elections scheduled for Jan 5 because they feared elections without a non-party caretaker government would not be free and fair.