The New Delhi-based Asian Centre for Human Rights (ACHR) said in a report released on Monday that 1,504 people died in police custody and 12,727 in judicial custody across the country over 10 years.
"A large majority of these deaths are a direct consequence of torture in custody," the ACHR said. "These deaths reflect only a fraction of the problem with torture and custodial deaths in India."
The ACHR collated statistics from India's National Human Rights Commission (NHRC), an independent body established by the government in 1993.
"Torture remains endemic, institutionalised and central to the administration of justice and counter-terrorism measures," the report said, urging the government to demonstrate the "political will" to end the abuse.
The report also criticised the NHRC for registering only six deaths in police custody in the insurgency-hit Muslim-majority Kashmir region during the past decade.
Kashmir Chief Minister Omar Abdullah stated this year that more than 341 people had died in police custody since 1990, it noted.
Custodial deaths are seen as a major problem in Kashmir, but the ACHR report detailed alleged torture across India, highlighting that 250 people died in police custody in the western state of Maharashtra between 2001 and 2010.
The ACHR said almost all deaths in Indian police custody happened within 48 hours and were due to torture, while judicial custody deaths were also due to poor medical facilities and "sub-human conditions" in jails.
In one case study, the report said Sanjay Nishad, 22, and Ashok Nishad, 30, died after being taken to a police station in Uttar Pradesh in February 2010.
They were accused of firing on a police constable, and their families said their injuries proved they were beaten through the night with sticks and rifle butts.
The Indian government has not commented on the ACHR report.
In July, Home Minister P. Chidambaram rejected accusations of torture within the judicial system after Denmark refused to allow the extradition of alleged arms trader Kim Davy on the grounds he may be treated inhumanely.