The plane went down near Jomsom Airport in western Nepal on a flight from Pokhara.
Earlier reports from officials had said as many as 19 people died.
The survivors, including two girls, were rescued from the debris of the Dronier aircraft, which broke up after striking the mountain, Press Trust of India reported. The plane did not catch fire.
The passengers were traveling to the holy shrine of Muktinath, Indian Embassy spokeswoman Apoorva Srivastav said.
"We are in touch with ... relatives of the families," she said.
Agni Air is a small Nepalese airline started in 2006. Its headquarters are in Kathmandu.