G Parameshwara, home minister in the southern state of Karnataka, claimed the “unfortunate” attacks in the city of Bangalore were a consequence of women wearing Western clothing.
He told the Times Now television network: “A large number of youngsters gathered – youngsters who are almost like Westerners.
“They try to copy Westerners not only in mindset, but even the dressing, so some disturbance, some girls are harassed, these kind of things do happen.”
Police have not charged anyone in connection with the assaults on Saturday night, but are looking through CCTV to try and identify the attackers.
Local media has shown images of victims cowering from attackers or fleeing for their safety in the city.
Mr Parameshwara later claimed to have been misquoted, but has been widely condemned for his comments.
Kiren Rijiju, the central government’s junior home minister, said on Twitter: “We can’t allow the shameful act of #MassMolestation to go unpunished.”
He added that women’s safety is a “must in a civilised society”.
Lalitha Kumaramangalam, chair of the National Commission for Women in India, called for Mr Parameshwara to resign.
She said: “I want to ask this minister: are Indian men so pathetic and weak that when they see a woman in western clothes on a day of revelry, they get out of control?
“When will the Indian men learn to respect women? The minister should apologise to the women of the country and resign.”
Bangalore police have said no complaints have been filed about the assaults.
India has seen a number of highly publicised incidents of sexual assault and violence against women.
In December 2012, a woman was gang-raped on a bus in New Delhi and later died from her injuries. That year’s New Year celebrations were officially cancelled after the attack.