He apologised for the remark, but it was roundly criticised.
Sinha, speaking at a CBI conference, was making the case for legalised sports betting. He then sought to counter any claim that legalising such an activity was useless without proper enforcement.
He said: “It is very easy to say ‘if you can’t enforce it’. It’s like: ‘if you can’t prevent rape, you enjoy it’.”
“It is better to have something, legalise it and earn some revenue, rather than throwing your hands up and let things happen.”
Sinha sought to explain his comments, which civil campaigners and opposition politicians said risked trivialising rape and raised questions over the CBI’s ability to investigate serious sexual assault cases.
“I regret any hurt caused,” Sinha said in a statement after the original remarks dominated news channels. “I gave my opinion that betting should be legalised and that if the laws cannot be enforced, that does not mean that laws should not be made.
“This is as erroneous as saying that if rape is inevitable one should lie back and enjoy it. I reiterate my deep sense of regard and respect for women and my commitment for gender issues.”
It comes with sexual violence under the spotlight in India. A young woman died last year after being gang raped on a bus in Delhi.
Kavita Krishnan, an activist with the All India Progressive Women’s Association, called for Sinha to step down.
“How can he remain the head of India’s premier investigation agency?” she said.
Nirmala Sitharaman, spokeswoman for the main opposition group, the Bharatiya Janata Party, called the remarks “shocking”.
“Wonder if his colleagues in the Bureau, his family and well-wishers approve of his view,” she wrote on Twitter.
There were more than 24,000 reported rapes in India in 2011, but activists say the real number is many times higher.
Following a public outcry over the Delhi attack, India introduced tougher rape laws in March, which include the death penalty for repeat offenders and for those whose victims are left in a “vegetative state”.
The CBI, which is similar to the Federal Bureau of Investigation (FBI) in the United States, was set up to fight corruption by government employees, but also investigates other important cases, including murder, rape and terrorism.