He says international sanctions on top junta officials bar Bangladesh from wider engagement with the Myanmar military
The victims are bank official Arman-uz-Zaman, 42, his wife, a Dhaka College teacher Afroza Parveen, 35, and their son 'Triman', 5.
They were admitted to Dhaka Medical College Hospital (DMCH) after the incident on Saturday night.
DMCH police camp ASI Sentu Chandra Das said they live in a flat on the top floor of a six-storey building at Green Road.
Police suspect the fire originated from a leak in the gas line.