A 10-year-old Chinese boy jumped 30 floors to his death after failing to write a self-criticism letter demanded by his teacher, state media reported Thursday.

The fifth-grade primary school student had been ordered to write a 1,000-character apology by his teacher for talking in class, China National Radio (CNR) reported on its website, citing a neighbour.

The educator allegedly told him to jump out of a building after he failed to complete the task, the report quoted relatives and the neighbour as saying.

"Teacher, I can't do it," was found written in one of his textbooks, CNR said. "I flinched several times when I tried to jump from the building."

The child smashed into a parked car beneath the flat where his family live, the West China City News reported.

His furious relatives posted a banner outside the school in the southwestern city of Chengdu reading: "The teacher forced our kid to jump off the building," pictures showed Thursday.

"The police investigation is still under way," an official of Jinjiang district, where the incident happened, told AFP, declining to comment further.

Strict discipline is an essential part of China's education system and culture, and tradition demands deference to authority, putting children under pressure to obey instructions.

The news provoked sadness and sympathy on Sina Weibo, a Chinese equivalent of Twitter.

"How can a guy like this be a teacher?" wrote one poster. "Who gave him the right to speak in this way? Why does the student have this kind of blind obedience?"

The boy's school said Thursday on its verified account that the child and some of his classmates had been ordered to write reviews of their behaviour after they disturbed a speaking competition.

He died "by accident", it said.