Gowda, who is also JD(S) president, said it was one of the "tragic moments" for Indians and "the government of India should take strong steps. That is my only demand.
"Government must take a firm stand to protect the honour and dignity of every citizen of the country," he told reporters.
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US Secretary of State John Kerry has expressed regret over the incident, but India-born prosecutor Preet Bharara has defended her arrest on December 12 on visa fraud charges.
On the Lokpal bill passed by Parliament, Gowda said, "I welcome this move. There are no two opinions on that. It was a matter that was pending for several years. Happy that it has finally taken shape."
On Aam Admi Party's exercise to take public opinion into account on government formation in Delhi, he said it was up to the AAP chief and the party's elected members to decide.
Gowda also accused the Siddaramaiah government in Karnataka of giving shelter to "land mafias" who had encroached on government lands and lakes in and around Bangalore.