The organisation concluded that India condoned torture in the region.
There has been no comment from the US. The ICRC said it was investigating.
The chief minister of the state of Jammu and Kashmir, Omar Abdullah, told India’s NDTV channel that the allegations related to a period before his government took power and that he did not condone torture.
SM Sohai, inspector general of police in Indian-administered Kashmir, said the reports were baseless “propaganda”.
“I do not how the Red Cross could have accessed that information because, normally they would not have access to these kind of locations, so it’s completely unfounded,” he told the BBC.
“Torture doesn’t happen… Where can it happen?”
Correspondents say the revelations will be embarrassing for Delhi, coming at a time of heightened sensitivity in Kashmir, which is divided between Indian and Pakistani control.