The floods and landslides sent a wall of water and debris crashing down a river between China and Nepal, burying buildings in mud.
"Entire villages and market areas have been wiped out," David Fisher, the Nepal head of the International Federation of Red Cross and Red Crescent Societies (IFRC), said in a statement.
The IFRC said it had released $1.4 million (1 million Swiss francs) in emergency funding to support relief operations.
Initial assistance includes drinking water and emergency supplies such as blankets, first aid kits, stretchers and body bags, it said.
"The priority now is to reach affected communities and get assistance to people who have lost their homes, suffered injuries or have been cut off," Fisher said.
The European Union said it had activated its Copernicus satellite surveillance system to help recovery efforts after the floods in Nepal, and was ready to provide more help, while the World Health Organisation said it had dispatched emergency medical supplies.
Neighbouring India sent an initial 10 tonnes of humanitarian assistance, including blankets, solar lamps and medicines, New Delhi's Subrahmanyam Jaishankar said.
India's Air Force said further military transport aircraft would carry more relief supplies, with "helicopters earmarked for rescue and evacuation operations".
Prime Minister Narendra Modi earlier said that India was "ready to provide all possible humanitarian assistance to Nepal".
The floods hit Nepal's northern border areas and China's Tibet region.
Penpa Tsering, leader of the India-based government of Tibetans in exile -- the Central Tibetan Administration (CTA) -- called the disaster a "catastrophe".
"The news of casualties and widespread destruction ...and of the hundreds still missing, is heartbreaking," Tsering said.
China calls the exiled Tibetans "nothing but a separatist political group".
India, downstream of Nepal, has also put rescue teams on high alert in the bordering states of Bihar and Uttar Pradesh, Home Minister Amit Shah said.
Bangladesh, another downstream nation, said it was "ready to assist Nepal in any possible way in relief and rescue efforts."
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