The Congress protestors lashed out at Eshwarappa and demanded his resignation.
"He doesn't know how to speak; he has used vulgar words which are not correct, he should leave politics," said a protestor.
"I don't think the Home Minister or the Chief Minister consider everyone as their own. Maybe when their own daughters are raped they might act differently," he had earlier said.
The BJP leader's comment came in wake of the rising crimes against children in Bangalore.
Eshwarappa, however, later clarified his statement.
"I requested that the Chief Minister and the Home Minister should give importance to women's safety. You see the press-meet of this morning," he said.
Bangalore has recently witnessed an increase in the number of cases of sexual assault against minors.
Earlier on Sunday, the Bangalore Police had arrested the principal and one of the directors of the private school where a six-year-old child was allegedly raped. A case of negligence was filed against the institution for not following the guidelines issued for children's safety.
This was the third such incident in recent months that has taken place within school premises in Bangalore.
A three-year-old child was allegedly raped at the private school she attended by a school teacher late on October 21.
In July, a school coach was detained over an alleged sexual attack on a six-year-old girl that had prompted protests by parents for several days. Barely a month later, allegations of a 63-year-old teacher assaulting an eight-year-old child in school premises over a period of time, surfaced.