But they warned that longer-term assistance for millions of survivors, many of whom have lost everything and have no food or clean water, would be vital.
"At this time we will welcome support from the international community," said a statement from the Bangladesh foreign ministry.
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We are doing as best as we can do ourselves."
The government said international aid worth about $120m has so far been promised, but that relief items such as tents, rice and water have been slow to reach many of the survivors.
At Patharghata, a trading town along the Bay of Bengal, more than 100 women gathered on Tuesday hoping to receive aid.
"I've been waiting here for several hours hoping to get some food and drinking water," said Safura Begum, who has three children. "But I am not sure it will come.
"Some biscuits and a few bottles of water are what I have got in the past three days."
Villagers in some of the country's most remote areas, where virtually every home was washed away, said they were worried about how they would re-establish their livelihoods.
In Padma, a small fishing town in the south, the wooden trawlers that the population relied on to make a living were smashed to bits by the storm.
"In about 30 minutes we all became paupers," said Abdul Jalil, a fisherman, who lost two fishing trawlers in the cyclone.
Jalil's mother, son, and a nephew all died in the storm, the worst to hit Bangladesh in a decade.
Significant damage
Douglas Casson Coutts, the World Food Programme representative for Bangladesh, said the extent of the devastation would make it difficult for people to rebuild their lives.
"There is significant damage to the infrastructure. There will definitely have to be longer term assistance to get people on their feet again."
Heather Blackwell, the Bangladesh head of the British aid group Oxfam, said: "People here are resilient. However, the scale is such that it will take months for people to be able to return to their normal lives."
Officials said the armed forces were continuing to work side by side with aid agencies to deliver relief by air, road and sea to remote places.
While the official death toll stands at over 3,000, disaster officials have suggested the toll could rise to 10,000 people once rescue workers reach the more remote areas.