The aircraft from Kathmandu-based Mountain Helicopters came down in a forested area north of the capital, police said.
"The helicopter crashed at 4:30pm in Sindhupalchowk district after it hit electricity lines, according to villagers there," said local police official Dipak Kharel.
Read: Schools reopen in quake-devastated Nepal
"Our troops have reached the site and found four bodies," Major-General Binoj Basnyat told AFP.
Relief teams from around the world have been working to provide water, food, shelter and medical assistance to Nepal since a 7.8-magnitude quake struck on April 25.
On May 12 a second major earthquake hit the country, the same day that a UH-1Y Huey helicopter came down on an aid mission in the north of the country. Six US Marines and two Nepalese soldiers were killed.
Read: Eight dead in Nepal chopper crash: US defence chief
More than 8,600 people died in the quakes, which destroyed more than half a million homes and left huge numbers of people without shelter with just weeks to go until the monsoon rains.
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