On Wednesday, Sinha said that his comments had been taken out of context and misinterpreted, and that he was sorry if he had caused hurt.
Angry activists, however, called for his resignation.
Communist Party of India (Marxist) leader Brinda Karat said Sinha's comments were offensive to women everywhere.
"It is sickening that a man who is in charge of several rape investigations should use such an analogy," Karat told reporters. "He should be prosecuted for degrading and insulting women."
The New Delhi attack on the young woman last December caused nationwide outrage and forced the government to change rape laws and create fast-track courts for rape cases. New laws introduced after the attack make stalking, voyeurism and sexual harassment a crime. They also provide for the death penalty for repeat offenders or for rape attacks that lead to the victim's death.