Rescue helicopters flew into the region to help and security forces on the ground were digging out the dead and survivors from the rubble, Nepal police spokesman Kuber Kadayat said.
Authorities said the death toll would rise as communications were cut off with many places, AP reported.
Troops were clearing roads and mountain trails that were blocked by landslides triggered by the earthquake. Helicopters flew in medical workers and medicines to the hospitals there.
Prime Minister Pushpa Kamal Dahal flew in by helicopter with a team of doctors. Mr Dahal led an armed communist revolt in 1996-2006 that began from the districts that were hit by the quake.
In Jajarkot district, the quake’s epicentre, 92 people were confirmed dead and 55 others injured, Mr Kadayat said.
The quake killed at least 36 people in neighbouring Rukum district, where houses collapsed, and at least 85 injured people were taken to the local hospital, he said.
At the regional hospital in the city of Nepalgunj, more than 100 hospital beds were made available and teams of doctors stood by to help the injured.
“I was fast asleep when all of a sudden it started shaking violently. I tried to run but the whole house collapsed. I tried escaping but half my body got buried in the debris,” said Bimal Kumar Karki, one of the first two people to be brought to the regional hospital.
“I screamed, but every one of my neighbours were in the same situation and screaming for help. It took nearly a half-hour to an hour before rescuers found me,” he said.
Security officials worked with villagers all through the night in the darkness to pull the dead and survivors from fallen houses.
The quake, which hit when many people already were asleep in their homes, was felt in India’s capital, New Delhi, more than 800 kilometres away.
The US Geological Survey said the earthquake had a preliminary magnitude of 5.6 and occurred at a depth of 11 miles. Nepal’s National Earthquake Monitoring & Research Center said its epicentre was at Jajarkot, which is about 400 kilometres north-east of the Nepalese capital, Kathmandu.
Earthquakes are common in mountainous Nepal. A 7.8 magnitude earthquake in 2015 killed some 9,000 people and damaged about 1 million structures.
Neighbouring India offered to help in the rescue efforts.
Indian Prime Minister Narendra Modi shared on social media that he was deeply saddened by the loss of lives and damage due to the earthquake in Nepal.
“India stands in solidarity with the people of Nepal and is ready to extend all possible assistance,” he said.