Police headquarters on August 1 instructed field units to strengthen security around police vehicles and premises.
The message said members of extremist groups or other offenders could target police jeeps, pickups and buses.
It directed personnel to park temporarily stopped vehicles in secure, monitored locations and to increase patrols and surveillance at police facilities.
On August 2, Dhaka Metropolitan Police Additional Commissioner Mohammad Shafiqul Islam said the instruction was not based on specific intelligence of an attack on law-enforcement personnel.
He described it as a routine reminder intended to keep police personnel more alert.
Shafiqul Islam linked the renewed caution to recent bomb-related concerns and what he described as false rumours.
Police headquarters media official AHM Shahadat Hossain said similar instructions are issued routinely to keep members active and alert, and said there was no reason for panic.
Shafiqul Islam said the Counter Terrorism and Transnational Crime unit was investigating a suspicious umbrella incident in Motijheel, while the Detective Branch was conducting a parallel inquiry.
Police said an improvised explosive device was recovered and defused beneath Motijheel Metro Rail Station on July 24.
Police also said suspicious items later found near Bangladesh Bank and at Mirpur-10 and Farmgate metro stations contained no explosives.
No group or individual has been publicly identified in connection with the Motijheel inquiry, and Shafiqul Islam said the investigation was continuing.