As Mr Tripathi met with women students at a university hostel on Wednesday night, he was asked whether he and other officials of the university had followed their "dharma" or duty in dealing with the protests.
"Yeh batao, kya ladkiyon ne dharm ka paalan kiya ki ek ladki ki asmita ko leke woh bazaar main nikal gayeen? (You tell me, did the girls follow their dharma by going to the market (with the modesty of a girl?)," Mr Tripathi shot back, apparently suggesting that the students were making a public spectacle of their friend's allegation that she was molested on campus.
BHU students have been protesting since last week over the alleged molestation; they allege that security on the campus is far from adequate and the university officials have only trivialized their concern. Mr Tripathi had called the woman's allegation as "just a case of eve-teasing".
Last Saturday, a woman protester was beaten by policemen called in when the students tried to meet the Vice Chancellor. The act was caught on mobile footage and became viral, causing outrage.
Mr Tripathi, who retires in two months, met the protesters for the first time since the crisis exploded. He called the meeting just after his trip to Delhi for a university executive council meeting and amid speculation that may be asked to go on leave.
Earlier this week, the University's proctor quit citing "moral grounds" after a report blamed the university for handling the protests poorly and also for being insensitive.
For the first time in its history, the prestigious university has a woman proctor. Assistant professor Royona Singh has said her priority will be to ensure the safety of women students on campus and reverse any restrictions that are unfair to them.
Women students have been protesting early hostel curfew and other examples of what they call discrimination - like only vegetarian food in their hostel mess.