Hasina asked the cabinet members to send her message to the local administrations that they have the authority to impose restrictions, Cabinet Secretary Khandker Anwarul Islam said after a meeting on Monday.
The coronavirus situation was largely explored before the meeting in separate discussions, Cabinet Secretary Islam said.
The local government, armed forces, law enforcement and other agencies have been told that they can meet locally and decide to impose and enforce restrictions or make the decision to increase treatment capacity if there are too many new cases in an area, he added.
“It's a government decision that if local authorities meet and decide to close an area, they can do so after discussing the issue.”
The cabinet secretary said the number of new cases had increased in Dinajpur, but fallen slightly in Jashore and Chanpainawabganj.
Asked whether any further decisions had been made about the nationwide lockdown restrictions, Islam said it was too early for the issue to be brought up.
Government offices had divided up the workload so that only half of the employees needed to be at the office at any one time as per the current restrictions, he said.