Desperate living conditions, and fears of disease and a breakdown in law and order in the aftermath of Saturday's earthquake in Nepal, have sparked an exodus from the country's capital.

More than 100,000 people have already left Kathmandu, with officials estimating the number could reach 300,000, more than a 10th of the city's population.

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Nepalis in the capital clashed with riot police and seized supplies of water as anger boiled over after buses promised by the government failed to materialise.

At a checkpoint on the main highway out of Kathmandu, officials said more than 300 packed buses and coaches had passed since 5 am on Tuesday, nearly 10 times the usual number.

Most were heading for distant regions, where most Kathmandu residents are originally from. "They keep coming. I've never seen it like this," said city official Tara Bhattrai. "They are going to all destinations".

The government has laid on free transport and many companies are changing their ticket prices.

"I'm afraid that in Kathmandu, life is a struggle. We have a rented home here but our own house is in the west, which was spared from the earthquake. My parents are very worried about us," said Lokraz Pant, a 20-year-old engineering student.

Sarlahi Singh, 30, a government scientist, said: "I'm going home where there is food and safety. There is no food here and no government support."

food and safety. There is no food here and no government support."

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A makeshift camp at Tunshikel in Kathmandu on Tuesday. Photograph: Buddhika Weerasinghe/Getty Images

Thousands of people formed a line around Kathmandu's Constituent Assembly Building looking for bus coupons that would take them to their respective homes outside Kathmandu valley.

Fearful of epidemics and aftershocks, they were told that the government would provide free buses to different parts of the country.

Sarmila Panthi, 24, joined the queue at around 2am in the hope of returning to her home in Dang district in western Nepal.

But after waiting for hours with no food and water, she has yet to secure a ticket. "It's been almost eight hours since I got here with my one-year-old child," she said. "Life has become very tough. I have no water and can't even use a toilet."

AFP reported that riot police clashed with people angry over the slow distribution of bus tickets. Some protesters forced a truck carrying drinking water off the road and climbed on top of it, throwing the bottles into the crowd.

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Nepalese police push back residents who began protesting after waiting for hours in line to board buses from Kathmandu. Photograph: Prakash Nathema/AFP/Getty Images

Authorities have begun the urgent task of distributing food and water to survivors, but the relief effort is being held up by bad weather and landslides that have blocked access to remote areas that were hit hardest by the disaster.

Five days after Nepal was hit by its worst earthquake in more than 80 years, vast numbers of displaced people queued patiently for emergency supplies, while residents of far-flung villages that have been reduced to rubble still wait for help.

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As the country began three days of national mourning, the prime minister, Sushil Koirala, warned that the death toll – now at 5,507 – could eventually rise to more than 10,000. About 8,000 people have been injured.

The UN estimates that eight million people have been affected by the quake – more than a quarter of Nepal's population – and that 1.4 million are in need of food assistance. Tens of thousands have been left homeless.

Meanwhile around 250 people are feared missing after an avalanche hit a popular trekking route on Tuesday.

"An avalanche occurred in the afternoon today in Ghodatabela, an area on the popular Langtang trekking route," near the quake's epicentre, said chief district officer Uddav Prasad Bhattarai.

"It is difficult to say how many are missing, but a preliminary guess is that about 250 might be missing."

Bhattarai said foreign tourists may have been among those missing after the avalanche, but details remained scant as the area is remote and communications difficult.

All climbers on the Nepal side of Mount Everest have left the mountain and the climbing season is over, according to guiding companies and individual climbers, after dozens of climbers were killed or injured when an avalanche swept across the basecamp area.