"There should be a time-bound and speedy investigation into cases registered with police stations," Kumar said at the meeting, according to an official release.
The review meeting was attended by state police chief P K Thakur, Principal Secretary (Home) Amir Subhani, and Additional Director General of Police (Headquarters) Sunil Kumar among others.
Kumar directed that probe after FIRs are registered at police stations should be expedited.
The recent murder of Aditya Sachdeva allegedly by the son of jailed suspended JD(U) MLC Manorama Devi and murder of a journalist at Siwan had brought the law and order situation in the state into focus.
Also some doctors have complained about receiving threatening call for ransom.