In a still-unfolding disaster, verified videos showed dozens of people swept away at the border, with authorities on both sides fearing far higher casualties and massive destruction.
Houses, roads and power projects were swept away in Nepal, while officials in Tibet said they feared "major casualties", with some missing in the county of Gyirong after a mudslide hit a border land crossing.
Initial reports suggested that an earthquake in the area could have triggered an avalanche and caused the floods, Nepal's foreign minister Shisir Khanal told the country's parliament on Wednesday, local media reported.
At least 384 travellers, including 105 Indians, 93 Nepalis, three US citizens and 12 British nationals were missing from the region, Nepal's tourism authority said.
South Korean news agency Yonhap separately reported that about eight of its nationals were also unaccounted for in Nepal.
Flood alerts were issued in the populous northern Indian states of Uttar Pradesh and Bihar as they border Nepal and several rivers flow down the mountains into their plains.
Security footage captured on the Chinese side of the Nepal-Tibet border showed many people fleeing before a wall of rock, mud and water destroyed buildings, vehicles and took many lives.
The exact cause of the mudslide could not be immediately determined, but the German Research Centre for Geosciences (GFZ) said there was a 4.4 magnitude quake about seven minutes before the time shown on the security footage time-stamp.
An ice-rock avalanche in the Lhende Khola river on the Nepali side was the trigger, but the cause remains unconfirmed, said Qianggong Zhang, head of climate and environmental risks, at the Kathmandu-based International Centre for Integrated Mountain Development.
"With a blockage still lodged upstream on the Nepal-China border river, authorities warn a second flood may occur," Qianggong said.
Rescue helicopters could not land in Nepal's affected areas of Syapru Besi and Timure in the mountainous district of Rasuwa, with a population of about 50,000, officials said, with the river flowing above its normal course.
Television images showed crumbled homes in the floodwaters, floating cars and a metal bridge being washed away, while witnesses told Reuters the waters engulfed entire villages.
"There could be heavy casualties or loss of property," said district administrator Narendra Pariyar, who urged dwellers on the banks of the Bhote Koshi river to move to higher ground, after reports of villages and project sites being swept up.
China's official Xinhua news agency said the mudslide occurred on the Nepali side and hit the Gyirong port, cutting roads, communications and power links in the Shigatse region near the border, but did not elaborate.
Chinese state broadcaster CCTV said authorities had deployed at least 574 rescuers to the Gyirong land crossing.
A rescuer told CCTV that it would take at least four hours for the team to reach the site due to the 1.5-metre sediment that blocked pathways leading to the affected area.
The debris had surged upstream from the Nepalese side of the crossing, the rescuer said.
President Xi Jinping urged "all-out" search efforts for the missing, as well as stronger monitoring and early warning systems to prevent secondary disasters.
Police and military were joining in the rescue effort, said Prime Minister Balendra Shah.
"Instructions have been given ... to move the people living in the lower areas to safer places," he said.
"People along the river are advised to exercise extra caution and remain alert."
Indian Prime Minister Narendra Modi said New Delhi was ready to provide all possible humanitarian assistance and teams form the two countries were co-ordinating closely on rescue and relief efforts.
