Food, fresh water and temporary shelter had still not reached many of the hungry and exhausted survivors.
"At this time we will welcome support from the international community," said a statement from Bangladesh Foreign Ministry. "We are doing as best as we can do ourselves," it said.
The government said international aid worth about US$120 million ( EUR 81.89 million) has so far been promised. But relief items such as tents, rice and water have been slow to reach most survivors of the worst cyclone to hit Bangladesh in a decade.
The American Red Cross said it will provide US$1.2 million ( EUR 819,000) to help get clean water to the survivors and build emergency shelters.
At Patharghata, a hard-hit trading town along the Bay of Bengal, more than 100 women - many of them clad in veils - gathered Tuesday hoping to get 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'm not sure it will come."
"Some biscuits and a few bottles of water are what I've gotten in the past three days," the 45-year-old said.
The government is using helicopters to get aid to the survivors - many of whom are still living out in the open. Some relief agencies are also using boats to ferry relief aid to remote pockets.
Catholic Relief Services are using ferries and traditional fishing boats to send food and emergency relief material to nearly 1,000 families in Barisal district, one of the hardest hit by the cyclone.
The cyclone that tore across the Bangladesh coast last Thursday has left tens of thousands of people homeless and desperate for help.
On Thursday night, Nasima Begum, 30, woke up to howling winds and high waves rolling from the sea into her thatched hut near Patharghata. Before her house collapsed she managed to gather her children and fight her way through the water to a nearby tree. She held on to the tree and asked the children to cling to her body.
"We were there for almost an hour before the storm subsided and the water began to recede. I don't know how I survived. But Allah has helped us," she said.
By Monday the official death toll stood at 3,113 after reports reached Dhaka from storm-ravaged areas that had earlier been largely cut off because of washed-out roads and disrupted phone services, said Lt. Col. Main Ullah Chowdhury, a spokesman for the army that is coordinating the relief and rescue work.
Local media reports say more than 4,000 people may have been killed. The Bangladesh Red Crescent Society, the Islamic equivalent of the Red Cross, has suggested the final figure could be around 10,000.
Every year, storms batter Bangladesh, a delta nation of 150 million people, often killing large numbers of people.
A similar cyclone in 1991 killed 139,000 people along the coast. The most recent deadly storm was a tornado that leveled 80 villages in northern Bangladesh in 1996, killing 621 people.