Roads leading out of the mountain valley city of one million were jammed with people, many with babies in their arms, trying to climb onto buses or hitch a ride aboard cars and trucks.
Huge queues had formed at Kathmandu airport, with people desperate to get a flight out.
Many said they had slept in the open since Saturday's quake, either because their homes were flattened or they were terrified that aftershocks would bring their houses crashing down.
A total of 3,218 people were confirmed killed in the 7.9 magnitude quake, a police official said on Monday, the worst in Nepal since 1934 when 8,500 died. More than 6,500 were injured.
Another 66 were killed across the border in India and at least another 20 in Tibet, China's state news agency said.
The toll is likely to rise as rescuers struggle to reach remote regions in the impoverished, mountainous country of 28 million people and as bodies buried under rubble are recovered.
As UNIAN reported earlier, according to the Ukrainian Foreign Ministry, at least 83 Ukrainian citizens in Nepal have not been in contact since Saturday’s earthquake.
