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KATHMANDU, Nepal — The death toll from the devastating 7.8-magnitude earthquake in Nepal surpassed 5,000 on Tuesday, as the government pushed back against criticism over a slow response.

Rescuers were still digging bodies out of the rubble in the capital Kathmandu, where centuries-old buildings were flattened by Saturday's quake and many people were sleeping outside for fear of further aftershocks.

Nepal's National Emergency Operation Center said the death toll had reached 5,057 and that nearly 11,000 people were injured in the quake. Officials have said it was impossible to tell how many bodies remained buried — meaning the death toll could continue to rise.

Amid criticism from some locals — many of whom have been using their bare hands to dig through rubble —Prime Minister Sushil Koirala said the government was doing everything in its capacity.

"The government is doing all it can for rescue and relief on a war footing," Koirala told Reuters. "It is a challenge and a very difficult hour for Nepal."

In the historic old city center of the capital, a crowd erupted in cheers on Tuesday as a dirt-covered man was pulled from the rubble and whisked away into an ambulance.

A Chinese rescue team also managed to pull a 21-year-old man out from the rubble after he had been trapped for 62 hours. Medics said his vital signs were good.

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Ross Prince, a 62-year-old Canadian tourist, was at the scene digging with his hands. Prince was on vacation when the quake struck — but said his focus immediately shifted to helping out with relief efforts.

"All you can do is…turn around and help the others," he told NBC News. "It's awful. We have to do something...It just tears you apart."

The earthquake, which also triggered a massive avalanche on Mount Everest that killed at least 18 people, was the deadliest to hit Nepal since a 1934 temblor took the lives of more than 10,000 people.

Around 450,000 people have been internally displaced by the disaster, according to the National Emergency Operation Center.

Since the disaster the air in Nepal has been filled with smoke from funeral pyres and wails fromfamilies mourning the ever-mounting dead.

Some 8 million people have been affected by the disaster — with 1.4 million in urgent need of food supplies, according to the United Nations.

Aftershocks and congestion on the tarmac at Kathmandu's airport initially slowed the arrival of critical aid as Nepal's supplies of food, water and medical equipment ran low.

With the threat of waterborne diseases looming, Oxfam's Nepal director Cecilia Keizer warned the population was in dire need of "immediate access" to safe water and sanitation facilities.

Among the international assistance sent to Nepal, a team of around 60 disaster zone experts from Virginia's Fairfax County Urban Search and Rescue touched down in Kathmandu on Tuesday.

While some grocery stores have reopened in the capital, banks and larger businesses remained closed, according to an operational update issued by the U.N. late Monday.

The U.N. said that with fuel running low, cars were lined up at gas stations; ATMs were still working but not being replenished; households that did have power were relying on generators, and cell network outages and overloads were also common.

Further complicating the relief effort, a heavy rainstorm broke out in Kathmandu on Tuesday and meteorologists were predicting more rain over the next 10 days.

Aid agencies said they still were struggling to reach more remote towns and villages in the country's mountainous, agricultural regions.

A team from the humanitarian charity Doctors Without Borders took a helicopter ride over 65 villages to the east, west and north of Kathmandu on Monday. They reported back that 45 — more than two thirds of these isolated communities — were damaged or completely destroyed.

The International Organization for Migration said on Twitter that aerial and satellite surveillance showed "whole towns" had been flattened.

In the mountainous Gorkha district, near the epicenter of the quake, helicopters crisscrossed the skies as rescuers ferried injured people and supplies to and from remote villages, The Associated Press reported.

Alexander Smith reported from London. NBC's Henry Austin, Reuters and The Associated Press contributed to this report.