Sidr, which triggered a six-meter (20-foot) tidal wave, swept away whole villages along the coast before ravaging a vast swathe of southern and central Bangladesh last Thursday evening.
The Red Crescent said on Sunday it expected the final death toll to be between 5,000 and 10,000.
Officials had Sunday night put the toll at 3,113 dead.
Five days after the cyclone hit, the number of dead was still unclear as many of the areas worst affected were remote and had not yet been reached by officials. Many bodies were also washed away by the tidal wave.
Some 138,000 people were killed by a cyclonic tidal wave in 1991 while a cyclone in 1970 killed an estimated half million people.
A network of cyclone shelters and an early warning system are credited with saving many lives in the impoverished and disaster-prone country.