Amulya had raised "Pakistan Zindabad" slogans thrice after the organisers, under the banner of "Save the Constitution", invited her to address the gathering in the presence of All India Majlis-e-Ittehadul Muslimeen (AIMIM) chief Asaduddin Owaisi, on Thursday.
After being removed from the stage, she was arrested on charges of sedition and produced before a magistrate's court, which remanded her to 14 days judicial custody.
Her father Wazi also called for action against her as per the law, saying she has made an "unforgiveable mistake."
On Friday, Yeddiyurappa said: "Importantly, the organisations that are behind people like Amulya and nurturing them, if we don't take action against such organisations, such things won't end."
Speaking to reporters in Mysuru, he said prima facie it was clear there was an conspiracy going on to disturb law and order with such incidents.
"If organisations that are behind her are inquired into, things will come out. It is clear she had links with Naxals in the past. In this backdrop, she should be punished and action taken against organisations that are behind her," he said.
The Chief Minister noted that the girl's father himself has said she should be punished and not get bail and that he would not seek protection for her.
City Police Commissioner Bhaskar Rao said "making a statement somewhere is different, but calling someone for a stage event and for them to make divisive comments, is it right?"
Action would be taken against the organisers, he said,
adding that those calling people for such events should take responsibility and them playing a 'drama' about their non- involvement in such incidents, is not acceptable.
"Because the matter is so sensitive, anything can happen any time," he said.
"We have been trying to maintain peace for three months in that it has become a competition to create a law and order situation," he added.
Home Minister Basavaraj Bommai said all angles, including the woman's posts on Facebook, would be looked into, including if any organisation was behind her.
"Let's look into what comes out of the investigation and accordingly action will be taken..." he said, as he hit out at the opposition for "supporting" such elements and asked them to function responsibly.
Amulya's father Wazi said action should be taken against her in accordance with law, so that she corrects herself.
"It is an unforgivable mistake, she has caused pain to Indians.I'm deeply disturbed....action should be taken against her in accordance with law. She is around 19, we will have to find out why she said it and who is behind it," he said.
"She is a bright girl....I have tried to tell her not to involve herself in such activities after I got to know she was involving in anti-CAA, anti-NRC protests and complete her education first," he said.
Meanwhile, a video of a group of people, allegedly right wing activists, last evening, purportedly questioning Wazi about his daughter's conduct and making him raise "Bharat Mata ki Jai" slogans has gone viral.
On the other hand a purported Facebook post of Amulya on February 16 has surfaced in which she has said 'Zindabad' to several neighbouring countries and that doing so does not make her belong to them.
"Hindustan Zindabad, Pakistan Zindabad, Bangladesh Zindabad, Sri Lanka Zindabad, Nepal Zindabad, Afghanistan Zindabad, China Zindabad, Nepal Zindabad... whichever country it may be,Zindabad to all countries,"said the post in Kannada.
Some people who are said to be Amulya's friends have claimed she was about to raise Zindabad slogans naming various countries as mentioned in the Facebook post before she was stopped by people around her on the stage.
However, others rejected such claims, pointing out that she had said Pakistan Zindabad thrice.
Several organisations staged protests in the city on Friday against the incident.
Business Standard has always strived hard to provide up-to-date information and commentary on developments that are of interest to you and have wider political and economic implications for the country and the world. Your encouragement and constant feedback on how to improve our offering have only made our resolve and commitment to these ideals stronger. Even during these difficult times arising out of Covid-19, we continue to remain committed to keeping you informed and updated with credible news, authoritative views and incisive commentary on topical issues of relevance.
We, however, have a request.
As we battle the economic impact of the pandemic, we need your support even more, so that we can continue to offer you more quality content. Our subscription model has seen an encouraging response from many of you, who have subscribed to our online content. More subscription to our online content can only help us achieve the goals of offering you even better and more relevant content. We believe in free, fair and credible journalism. Your support through more subscriptions can help us practise the journalism to which we are committed.
Support quality journalism and subscribe to Business Standard.