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 has been leading the country since 2009, to step down.
Ms Hasina is reported to have fled the country as anti-government protesters vowed to march to the capital to demand her resignation on Monday.
Broadband internet and mobile data services have been restored across Bangladesh after a blackout.