Singh also expressed "sincerest condolences" to the Government and people of Bangladesh.
"I am deeply saddened at the loss of life resulting from the fire in a garment factory outside Dhaka. I express to the Government and people of Bangladesh our sincerest condolences. Our thoughts and prayers are with the bereaved families," he said in a message here.
In one of the worst fire tragedies in the country, a blaze broke out at Tazrin Fashion factory in suburban Ashulia Savar, 30 km from Dhaka, last night and quickly spread to the ground and first floors of the six-storey building.
At least 124 people died in the fire incident.
