Police said the car veered onto the pavement after making "contact" with another larger vehicle that was turning at a junction in Otsu City.
The accident killed a girl and a boy, both two years old, a police spokesperson told AFP.
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"The (smaller) car rammed into a group of 13 nursery school children and three teachers who were walking on the pavement," the police said in a statement.
A police spokesperson said some of the rest of the group suffered injuries but could not give further details.
The children and their teachers were on the pavement near a crossing when the small vehicle crashed into them. Japanese nursery schools regularly take children to the local park for playtime or out on short excursions during the day.
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Footage on local media in the aftermath of the accident showed one car had veered up off the road and onto the pavement. A second car that appeared to have been damaged in a crash could be seen still on the road.
Police said they had arrested the drivers of both cars - a 52-year-old woman and a 62-year-old woman.
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