Police Headquarters issued a nationwide alert on 1 August over intelligence indicating that vehicles used by police could be targeted in attacks.
An urgent message from the Operations Control Room ordered all field-level units to reinforce security arrangements.
The instructions cover jeeps, pickups, buses and other vehicles used by police.
Vehicles making temporary stops while on duty are to be parked in the safest practicable location and kept under police observation.
Security is also to be strengthened for vehicles parked after duty at police stations, police lines, office compounds and other designated locations.
The message calls for regular patrols, necessary surveillance, heightened attention to suspicious people or objects, and immediate reporting of suspicious activity to senior authorities.
Police Headquarters spokesperson AHM Shahadat Hossain said such instructions are periodically issued to maintain security and keep police personnel alert, and said there was no reason for alarm.
A bomb was recovered from inside an umbrella beneath Motijheel Metro Rail Station on 24 July.
Police described that device as a powerful improvised explosive device and said it was defused; this characterization is supported by one item in the evidence set.
The following day, an unattended sack with an umbrella protruding from it near Bangladesh Bank caused concern.
Suspicious items were also reported at Mirpur-10 and Farmgate metro stations on 1 August, but the Dhaka Metropolitan Police bomb-disposal team found no explosives in either item.
An unidentified-person case under the Explosive Substances Act was filed over the Motijheel device, police said.
The evidence does not identify a person or group responsible for the Motijheel device, nor does it establish a link between the recent incidents and the warning concerning police vehicles.