Waker-Us-Zaman vowed to launch an investigation into the deadly crackdowns that fuelled outrage against the government as nearly 300 people were killed in protests over the past month.
Ms Hasina’s resignation came as student activists called for a march on Dhaka on Monday in defiance of a nationwide curfew, to press for her to quit.
At least 95 people, including at least 14 police officers, died in clashes in the capital on Sunday, according to local news, while hundreds more were injured.
At least six people were reportedly killed in clashes between police and protesters in the Jatrabari and Dhaka Medical College areas on Monday.
The demonstrations began with students seeking to end a quota system for government jobs, but clashes with police and pro-government activists escalated into violence that left more than 200 dead last month.
That triggered more protests demanding accountability from the government, which have grown into calls for Ms Hasina -who won a fourth straight term in January in an election boycotted by the opposition – to step down.
Thousands of opposition members were imprisoned as she sought to run for a fourth term.
Ms Hasina, the daughter of independence leader Sheikh Mujibur Rahman, is the longest-serving leader in the history of the predominantly Muslim country of 160 million people.
Before being elected in 2009, she had already been prime minister between 1996 and 2001.
Sheikh Hasina political opponents have previously accused her of growing increasingly autocratic and called her a threat to the country’s democracy.
Her father was assassinated in 1975 during an army coup. Most of his family members were killed, with the exception of his two daughters, Sheikh Hasina and Sheikh Rehana.
