India's Supreme Court on Tuesday called for fast-track investigations and special courts to hear child rape cases amid an upsurge in deadly sex crimes.

Authorities have been facing intense pressure to act since the rape and murder of an eight-year-old Muslim girl by a group of Hindus, and other cases.

After the rape of the girl in Jammu and Kashmir state made national headlines last month, the government changed the law so that child rapists can face execution.

A Supreme Court bench headed by Chief Justice Dipak Misra said Tuesday that trial courts must not grant unnecessary adjournments in such sensitive cases.

It also said state police chiefs should form task forces to investigate child rape cases, which must be heard by special courts.

"Efforts have to be made by high courts to provide child-friendly courts," the bench said.

The directives came amid public outrage in recent weeks over the rape and murder in Jammu that has put an increased spotlight on other near-daily cases.

Activists say the government does not take rape seriously. Accusations have mounted since new Kashmir deputy chief minister Kavinder Gupta called the Jammu rape a "small incident" just hours after being sworn in on Monday.

Anger has also grown over the case of a six-year-old girl who died in hospital at the weekend, a week after she was viciously attacked and raped at Cuttack in the northeastern state of Odisha.

India saw similar protests after the 2012 gang-rape of a student on a bus in New Delhi. She later died in hospital of her injuries.

The incident triggered weeks of street protests and global condemnation.

But sexual violence, including against children, remains unabated. Some 11,000 child rape cases were reported in 2015.