Hundreds of protesters rallied in central India for the third straight day on Friday over the brutal rape of an eight-year-old girl now battling for her life in hospital.

Crowds holding placards and chanting "death to the rapist" called for the man arrested over the assault to be hanged in several demonstrations across the Mandsaur district of Madhya Pradesh state.

The case recalls the 2012 gang-rape and murder of a student on a Delhi bus which sparked revulsion and protests across India and put the country's abysmal record on sexual violence in the global spotlight.

In the latest incident, the suspect allegedly picked up the child outside her school on Tuesday as she waited for her father, promising to take her home, police said.

Instead he allegedly took her to a secluded spot, where he brutally raped her and slashed her neck, leaving her to die. She was found by locals.

"She remains critical in an intensive care unit. She is unable to speak as her vocal chords have been damaged by a deep cut on her throat," a doctor treating her told AFP.

The physician, who did not want to be named, said the girl had internal injuries and underwent surgery.

The suspect is being interrogated and faces charges of rape and attempted murder, Mandsaur deputy police chief S. S. Kanesh told AFP.

Many local shops and schools remained closed as hundreds demonstrated across the district, including students who wore black armbands.

Police deployed officers in riot gear at several locations after angry protesters clashed with them late Thursday. 

"There have been several demonstrations but the situation remains under control," Kanesh told AFP. 

Sexual violence is rife in India with nearly 40,000 rape cases reported in 2016, which activists say is the tip of the iceberg as most cases go unreported. 

Madhya Pradesh reported the most rapes of any Indian state in 2016, with more than 4,900 cases reported, according to government data.

India in April made the rape of children up to eight years of age a capital offence.

That came after the gang-rape and murder of a Muslim girl by a group of Hindu extremists who, police say, wanted to drive away her family from where they lived in the northern Jammu region.