A police officer said the girls had an "intimate friendship" which their teachers felt was "inappropriate". Their parents had also been asked to counsel them in the past, he said.
It is not clear what really happened at school on Friday. But a teacher did tell the two girls to come to school with their parents the next day.
The two girls did not go back home.
When their daughters didn't return home after school, their parents complained to the police that they were missing.
"We tried to trace the girls on Friday but could not locate them," the officer in Salem district, over 350 km south of state capital Chennai said.
The next morning, the girls were seen jumping off the five-storied building by some people.

The scene outside the building in Salem district where 2 school girls jumped off a building