Officials and rescue workers believe the August 26 collapse of a glacier on the upper reaches of the Trishuli River trapped at least 900 people in tunnels related to six hydropower projects along the river.
At least 1287 people were killed in Nepal as houses, streets and schools in towns and villages near the border with China's Tibet were swept away. More than 5080 people are still missing and thousands more displaced.
China has put the death toll in Tibet at 21, with 541 others listed as missing.
The two workers pulled from the tunnel at the Upper Trishuli 3A Hydropower Station are the first to be rescued from the hydropower projects and have been taken to an army hospital in the capital Kathmandu.
The workers rescued on Friday were Sanjay Sah, a mechanical foreman, and Kabir Maharjan, a mechanical supervisor, Energy Minister Biraj Bhakta Shrestha's office said in a statement.
Videos and photos released by Nepali authorities showed Maharjan being pulled out of a hole in the ground amid cheering bystanders and put on a stretcher.
The other man, Sah, was carried out on the back of a worker to a rescue tent, his face covered in mud.
Sah told rescuers he spent time reciting mantras (verses from a prayer) while he was trapped, according to the Kathmandu Post.
He said three or four more people could be alive in the tunnel, and possibly more deeper in its reaches.
Maharjan cannot move his hands and legs but Sah's injuries are not critical, an aide to the energy minister told Reuters.
Amir Maharjan, Kabir's brother, said: "I have been hearing from the news that my brother has been found. The entire family is very happy."
More search and rescue operations were underway around the Upper Trishuli 3A project, the Nepali Army said. Rescue efforts were being led by the army and police, with assistance from experts from India, South Korea and China.
Property, housing and infrastructure worth at least 387.5 billion Nepalese rupees ($A3.55 billion) was lost in last week's catastrophe, Dharma Raj Upreti, chief of the National Disaster Risk Reduction and Management Authority, said on Friday.
Nepal will have to rebuild about 20,000 houses in flood-ravaged areas, authorities say, as rescuers continue to search for workers trapped in tunnels and thousands of missing people after last week's catastrophe.
A glacier collapse on August 26 sent a deluge of ice, rock and mud sweeping through the impoverished country's border region with China, wiping out settlements and villages and leaving few houses standing and undamaged.
"We anticipate that the resources required for rebuilding will be substantial," Foreign Minister Shisir Khanal told foreign ambassadors in Kathmandu.
Prime Minister Balendra Shah's cabinet set Monday, the 13th day after the disaster, as a day of mourning in Nepal, a cabinet spokesperson said.
In Hindu tradition, the 13th day traditionally marks the end of the formal mourning period.
An Australian medical student whose partner went missing near the Nepal-China border urged tech companies to do more to help find him and others caught up in the disaster by sharing tracking data that could narrow the search areas for rescue teams.
Sarada Viswanathan, 23, has spent the past eight days trying to piece together the last movements of her boyfriend Rishab Iyer and his family.
Viswanathan said obtaining information out of Nepal has been difficult, with Apple and Optus denying her requests for location data that could shed light on their whereabouts.
"We're all just scrambling to try and put the pieces together ourselves," she said.
"Their phones are most likely dead. They have no way of contacting us. We're really just begging for help."
At least 583 foreign nationals were missing in the floods, Nepal said, many of them pilgrims and trekkers.
Australian disaster response specialists left for Nepal on Friday to join the search for survivors, as the government there expressed "serious concerns" for the welfare of its 36 missing citizens.
with AP and DPA
