A rare one-horned rhinoceros killed a four-year-old girl and injured her 73-year-old grandmother in a village near a national park in Nepal, local police said on Monday.

The wild rhino entered the settlement of Sherganj in south-central Nepal early Sunday and killed the girl who was warming herself at a log fire outside her home, said local police inspector Shiva Acharya Sharma.

"Villagers fled their homes as the rhino chased them but the girl and the elderly woman were slow to respond and came under attack," Sharma said.

The girl's grandmother was admitted to a hospital in Bharatpur, the nearest town. 

Two weeks ago, a rhino killed a man aged in his forties in the same area.

Nepal's rhinoceros population, now estimated at 645, has significantly increased, but the rise in numbers has also led to more attacks by the animals, raising concerns about the safety of people living near protected areas.