Ashutosh Ranka and Saurav Das were among about a dozen people detained by police on Tuesday after they climbed over barricades to enter the grounds of Jantar Mantar, a historic observatory in central New Delhi that has long been a site for protests.
Police said the site was no longer an official protest venue and accused Das and Ranka of trespassing and defying prohibitory orders.
The arrests follow a sweeping police crackdown over the weekend aimed at preventing mostly young Indians from gathering in New Delhi to demand the resignation of Chief Election Commissioner Gyanesh Kumar. Police briefly detained thousands of demonstrators.
"Jantar Mantar belongs to the people of India. We will reclaim it," opposition leader Rahul Gandhi wrote on X in a post condemning the arrests as "an act of cowardice."
Protests have intensified over an ongoing nationwide revision of voter lists that has removed more than 130 million names since last year. Critics say the exercise is politically motivated and could disenfranchise millions of eligible voters.
The Election Commission and Prime Minister Narendra Modi's administration say the revision is intended to remove duplicate and ineligible entries.
Abhijeet Dipke, the "Cockroach" movement's founder, criticised Modi in a post on X.
"If you're so determined to crush dissent, have the courage to officially declare an emergency instead of hiding behind these cowardly tactics," Dipke wrote.
The "Cockroach" movement began as an online satirical campaign this summer after India's chief justice compared unemployed young people to parasites. Many young Indians embraced the remark, adopting the cockroach as a symbol of resilience.
Protests led by the group forced the resignation of Modi's education minister in July, a rare setback for the prime minister, who has been in power for more than 12 years.
