"The government is doing all it can for rescue and relief on a war footing," Prime Minister Sushil Koirala said. READ MORE: US praises India's role in helping quake-hit Nepal ALSO READ: PM Modi donates one month's salary for earthquake relief fund MUSR READ: A friend in need: China, India turn on aid diplomacy in Nepal
"It is a challenge and a very difficult hour for Nepal," he said.
International aid has finally begun arriving in the Himalayan nation of 28 million people, three days after Saturday's 7.9 magnitude quake, but disbursement is slow. According to the home (interior) ministry, the confirmed death toll stands at 4,349, with more than 7,000 injured.
"The death toll could go up to 10,000 because information from remote villages hit by the earthquake is yet to come in," Koirala said.
The United Nations said 8 million people were affected by the quake and that 1.4 million people were in need of food.
Nepal's most deadly quake in 81 years also triggered a huge avalanche on Mount Everest that killed at least 17 climbers and guides, including four foreigners, the worst single disaster on the world's highest peak.
All the climbers who had been stranded at camps high up on Everest had been flown by helicopters to safety, mountaineers reported on Tuesday.
A series of aftershocks, severe damage from the quake, creaking infrastructure and a lack of funds have slowed rescue efforts in the impoverished, mountainous country sandwiched between India and China. In the capital Kathmandu, youths and relatives of victims were digging into the ruins of destroyed buildings and landmarks.
"Waiting for help is more torturous than doing this ourselves," said Pradip Subba, searching for the bodies of his brother and sister-in-law in the debris of Kathmandu's historic Dharahara tower. The 19th century minaret collapsed on Saturday as weekend sightseers clambered up its spiral stairs.
"Our hands are the only machine right now," said the 27-year-old, part of a group of locals pulling out bricks and blocks of concrete with cloth masks over their faces to ward off the stench of rotting bodies. "There is just no one from the government or the army to help us."
Scores of people were killed in the collapse of the tower.
Elsewhere in the capital's ancient Durbar Square, groups of young men cleared rubble from around an ancient temple, using pickaxes, shovels and their bare hands. A few policemen stood by, watching.
Heavy rain later on Tuesday slowed down the rescue work.
The head of neighbouring India's National Disaster Response Force (NDRF), one of the first foreign organisations to arrive in Nepal to help in the search and rescue effort, said finding survivors and the bodies of the dead would take time.
NDRF Director General O.P. Singh said heavy equipment could not fit through many of the narrow streets of Kathmandu.
"You have to remove all this rubble, so that will take a lot of time ... I think it's going to take weeks," he said late on Monday.
"The government is doing all it can for rescue and relief on a war footing," Prime Minister Sushil Koirala said.
READ MORE: US praises India's role in helping quake-hit Nepal
ALSO READ: PM Modi donates one month's salary for earthquake relief fund
MUSR READ: A friend in need: China, India turn on aid diplomacy in Nepal