Shah said in New York that Nepal's recovery and reconstruction needs were estimated at about 10 per cent of gross domestic product following the flood that struck mountain communities four weeks ago.
He argued that vulnerable countries should not be forced to take on additional debt to rebuild from catastrophic climate events.
"When a climate-driven disaster destroys infrastructure of a poor country, the answer cannot simply be another mega loan or a patchwork of small grants," Shah said. "We need adequate grant-based support from the world."
He urged closer cooperation between Nepal, India and China on climate resilience, calling for an urgent Himalayan mechanism to share satellite data, monitor glacial lakes, strengthen early-warning systems and coordinate disaster responses across borders.
The Nepalese leader said the flood, which he described as a warning of the growing risks posed by climate change, had swept away roads, bridges, schools, homes and livelihoods, interrupting Nepal's development progress.
"We did not create this crisis, yet we are paying a colossal price for it," said Shah, who at 36 is the youngest head of government to address the General Assembly this year.
"Our glaciers are retreating, our mountain slopes are becoming unstable, our rivers are becoming less predictable, and every major disaster threatens to erase years of development."
The collapse of a glacier near the border between Nepal and China's Tibet Autonomous Region in late August triggered landslides and a flash flood that tore through valleys downstream. Weeks later, search and recovery operations were still under way, with more than 6000 people remaining missing in the area.
Shah said many of them may never be found.
The World Bank earlier this week made available up to $US170 million in emergency financing to help Nepal respond to the disaster and begin recovery efforts.
with AP