The Bangladeshi Prime Minister, Sheikh Hasina, said while on a visit to the affected areas: "We are not appealing for international help but of course will welcome [it] if anyone offers to assist."
This low-lying nation, already on a virtual flood "war footing", launched a massive rescue and relief operation in areas devastated by high winds and tidal seas on Monday.
Many stricken villages remained isolated, so official figures were incomplete, with the early confirmed death toll put at 95. But local newspapers said the cyclone, roaring in from the Bay of Bengal, had killed hundreds and damaged crops near harvest time.
The government-run Bangladesh Times said up to 500 people were feared dead. Other newspapers, quoting their own sources, put the death toll at more than 350, with more than 2,000 people injured in Chittagong alone.
Some 250 others had been killed in Cox's Bazar, one of the areas worst hit by the cyclone, the newspapers said.
About 100 fishermen from the coastal district of Patuakhali were missing at sea, newspaper reporters in Chittagong said. The known death toll so far was 95, government officials said: 50 in the city of Chittagong and a total of 45 at Bashkhali, Maheshkhali and Cox's Bazar.
The official figure for injuries rose to "thousands", the Cyclone Preparedness Centre in Chittagong stated. Earlier, it had claimed that more than 100 were injured. Army, naval and police units joined thousands of volunteers fanning out across coastal regions in south-east Bangladesh. The cyclone ravaged Chittagong, the Cox's Bazar and Tenkaf districts and several islands on Monday with 124mph winds.
The Prime Minister said she was happy over the way her government had handled the crisis. "The death toll has been fewer than feared. Rescue and relief operations are continuing smoothly," Ms Hasina said. She earlier assured her countrymen and women that there would be no dearth of help in the wake of the disaster.
Foreign aid agencies, including Care International and Oxfam, said they had yet to receive full reports from places battered by the cyclone, which tapered off by midnight on Monday. "Most of the disaster-hit areas have not been accessed yet. It's very difficult to get a clear picture immediately," one official said.
Disaster management officials said the death toll was "much lower than feared" because the the cyclone struck the coastline during low tide. "Otherwise the tidal surge could be much higher and might have swept over many low-lying islands," one official said.
Bangladesh's worst recorded cyclone, in 1991, killed at least 138,000 people and left millions homeless.
A navy vessel with relief supplies was sailing to Saint Martin's island, which was inundated by a six-foot tidal surge. Army helicopters were dropping supplies elsewhere.
Officials in Chittagong said power cuts since Monday had forced hundreds of water pumps to stop working, causing a severe shortage of drinking water.
They said nearly 400,000 houses had been damaged and 15,000 cattle killed. More than 1.5 million people were made homeless or affected otherwise, officials said on Tuesday.
Chittagong harbour had suffered substantial damage, port officials said without giving details. The Panamanian-flagged ship Esco Argo, which sent an SOS message during the cyclone saying it was sinking in the Bay of Bengal, was safe, the ship's local agents, Progoti Shipping Limited, said. "We feel the SOS was issued in advance amid an unpredictable situation," the agents added.
Agriculture officials said there had been some damage to rice crops but shrimp cultivation was more seriously affected.