But power blackouts in the capital city of Kathmandu, supply shortages and difficulties getting around complicated the efforts.
The United Nations estimated that the disaster had affected 8 million people across the Himalayan nation. More than 1.4 million people are in need of food assistance, the world body said in a situation report Monday.
CNN's Dr. Sanjay Gupta said doctors at one Kathmandu hospital had moved patients from the 120-year-old building and into another structure, where they were operating on patients in rooms normally not used as operating theaters.
Hospitals were running short on supplies despite international efforts to bring in aid. Numerous aid groups and at least 16 nations rushed aid and workers to Nepal, with more on the way.
And across the region, thousands prepared to spend another night outdoors, fearing that damaged buildings could collapse if there are more aftershocks.
The destruction in Kathmandu, the capital, is stark: revered temples reduced to rubble, people buried in the wreckage of their homes, hospitals short on medical supplies and overflowing with patients. Serious damage is also reported in villages in the surrounding valley.
But farther out across Nepal's rugged landscape -- closer to the epicenter of Saturday's magnitude-7.8 quake -- the situation is disturbingly murky.
"Information about remote areas is severely lacking at this time," said Devendra Singh Tak, an official with Save the Children, noting that roads were blocked and communications unreliable.
Reports of 'total or near total destruction'
Patchy reports have filtered through of entire villages leveled by the quake or engulfed by landslides.
"Some of the initial surveys that we're hearing of from the zones closer to the epicenter talk about total or near total destruction," said Jeremy Konyndyk, director of the Office of Foreign Disaster Assistance for the U.S. Agency for International Development.
Tak, who is in Kathmandu, said Save the Children and other aid groups were sending out teams Monday to more remote areas. The Nepalese government said it was flying helicopters to places it couldn't reach by road.
"That's where one needs to get out and conduct rescue and relief," Tak said.
UNICEF, the U.N. children's agency, said Sunday that nearly 1 million Nepalese children urgently need assistance.
China, India, France, Italy, Britain, Canada, the United States, Australia, Taiwan, Pakistan, the United Arab Emirates, Israel, Switzerland, Norway, Singapore and South Korea were among the nations sending aid and search and rescue crews. The European Union and the World Health Organization were also sending aid.
The United States announced Monday it would send $9 million, on top of the $1 million it had previously announced. That's in addition to 45 tons of aid, a USAID disaster team and a search and rescue team already dispatched to Nepal. A U.S. Special Forces team in Nepal for high-altitude training was also helping out, according to the Pentagon.
Video shows survivor pulled from rubble
Despite lengthening odds, rescuers continued to look for survivors.
On Monday, video posted to Facebook showed rescuers pulling a boy out of debris after three hours of continuous digging.
"Look up, look up, open your eyes," a rescuer says to the boy.
Hopes of finding many more people alive appeared to be fading as vital hours ticked by.
The death toll in Nepal stood at 4,352 Tuesday morning, according to the country's Home Ministry. Another 72 people died in India, while China reported 25 deaths. More than 8,000 people have been injured, authorities said.
Most of the casualty numbers in Nepal are believed to have come mainly from Kathmandu and the surrounding area. They are expected to rise further as information emerges from more remote areas.
Panorama of devastation
The earthquake and its aftershocks have turned one of the world's most scenic regions into a panorama of devastation.
"The journey towards my family home in Sitapaila was a map of quake destruction, with many houses -- old and new -- torn apart," wrote freelance journalist Sunir Pandey.
"A high wall surrounding a monastery had collapsed and the nuns had run to a nearby field," he wrote. "A mud-and-brick cottage had fallen on a blue motorbike but no trace could be found of its rider. Everywhere, survivors gathered wherever they could find open space -- fields, private compounds, empty roadside lots."
At night, many Nepalis slept outside, shivering in the frigid air of the Himalayan Mountains but at least safe from falling debris.
"Even people staying in hotels, they carried their blankets and pillows and were sleeping either on the ground floor or out in the open," Tak of Save the Children said.
Residents of Kathmandu are banding together to get by, with stores shuttered and very few sources of food and drinkable water. People have independently set up communal kitchens for cooking.
Destruction of temples strikes spiritual blow
Many of the city's centuries-old buildings, which had survived countless earthquakes over the generations and provided a sense of national pride, have been toppled.
The destruction of many important temples in the heart of Kathmandu has deepened the despair many Nepalis are experiencing. Religion is an important part of life in the mainly Hindu nation.
The iconic buildings, which are often the first stop of any tourist's tour of the city, crumbled before the eyes of onlookers as the quake struck Saturday.
Police officers and volunteers continued to pick through the temples' rubble on Monday, using their bare hands, shovels and pieces of metal. They shunned the use of heavier gear to dig through the wreckage for fear of harming any survivors, bodies or priceless artifacts buried within.
Tourism has been one of the few economic bright spots in Nepal, one of the poorest nations in the world. But now that industry is threatened after the earthquake, which set off deadly avalanches on Mount Everest, the country's most famous attraction.
Damage to climbing infrastructure on the mountain, not to mention the overall situation in Nepal, means the climbing season is over for the year, climber Jim Davidson told CNN from the Everest base camp, where he was evacuated after spending two days on the mountain.
China has canceled all climbs on its side of the mountain, the Xinhua news agency reported Monday.
Tourism directly accounts for about 4% of Nepal's gross domestic product and indirectly contributes to 8%, according to IHS Asia Pacific chief economist Rajiv Biswas.
All told, the earthquake could cost Nepal $5 billion, Biswas estimated Monday -- a huge hit against its gross domestic product of $19.3 billion in 2014.
Relief effort faces challenges
Humanitarian workers say medical supplies are reported to be scarce. Doctors at Kathmandu's overcrowded hospitals are appealing for help.
"I've seen a lot of situations around the world, and this is as bad as I've ever seen it," said CNN's Gupta, a neurosurgeon.
"They need more resources, they need more personnel here right now, and they're expecting many more patients as these rescue operations go on."
International efforts are well underway to send aid into Nepal, but it was unclear whether enough was trickling through to the places that needed it most.
Some aid flights were delayed Sunday after a big aftershock hit Nepal. The country's mountainous terrain makes it harder to move supplies far beyond the capital.
A CNN team at Kathmandu's main airport on Monday saw large numbers of cargo planes on the tarmac, but also witnessed chaotic scenes as officials struggled to cope with the influx of aid and the large numbers of people trying get out of the country.
The airport was also facing some of the shortages afflicting the disaster-hit nation.
"Even at the airport in Kathmandu, there is no drinking water or food or other provisions available, so one can imagine what might be happening in other parts of the country," said Tak of Save the Children.