Indian police briefly detained the opposition leader, Rahul Gandhi, during protests on Tuesday calling for the resignation of the prime minister, Narendra Modi, in solidarity with the new youth-led “cockroach” movement.

Gandhi, the leader of India’s Congress party, was forcefully removed by police as he staged a sit-in outside Modi’s house on Tuesday afternoon, accusing the prime minister of “destroying the future of India’s youth”.

Footage showed police holding the opposition leader by his arms and legs as they pushed through large crowds. They forced Gandhi into a nearby bus and removed him from the area. Chaotic scenes ensued as protesters appeared to try to board the bus as it sped away.

His sister, Priyanka Gandhi, a senior party strategist, was also briefly detained on Tuesday. Police confirmed they were later released.

Police detain India’s opposition Congress leader, Priyanka Gandhi, outside the prime minister’s residence in New Delhi, India. Photograph: Ritesh Shukla/Getty Images

Gandhi’s detention took place as thousands of people gathered at a separate site in central Delhi that has become the heart of youth-led protests calling for education reform and the resignation of the education minister, which have continued to gather momentum.

The newly formed Cockroach Janata party (CJP), a youth-led movement that began as a satirical online joke, had mobilised on Monday one of the biggest anti-government protests in years, where police acted with brutality, using teargas and batons, leaving dozens injured.

The CJP has demanded changes to India’s education system and the resignation of the education minister, Dharmendra Pradhan, after repeated scandals over testing, but has also grown into a larger movement giving voice to the frustration’s of India’s youth.

Amid gruelling heat and humidity, hundreds of young protesters remained camped out at the CJP’s protest site in Delhi on Wednesday morning, many of whom had travelled for miles and had slept out overnight.

Food deliveries sent by supporters – some ordered from abroad – have continued to arrive at the site, keeping the protesters well fed on biryani, pizza, rice and dal. Morale remained high as slogans and songs rang out across the site.

A Cockroach Janta party supporter holds a placard amid a protest in New Delhi on 22 July. Photograph: Sajjad Hussain/AFP/Getty

It was estimated that upwards of 50,000 protesters had turned out on the streets of Delhi on Monday, even though the police denied permission for them to march on parliament. While it began as a peaceful demonstration, by late afternoon police began to unleash violence on the protesters.

Police said 60 civilians had been injured and another 118 police personnel were hurt, accusing protesters of instigating the clashes. But organisers condemned the “high-handedness” of the authorities and said that hundreds of peaceful protesters had been injured at the hands of the police, including at least one woman now on a ventilator in the ICU from her injuries.

Congress accused the Modi government of refusing to address the issues of the students and the alleged “brutality unleashed on students” in parliament.

On Tuesday, Ghandi said: “The government doesn’t want to take any accountability, nor does it want to have a debate on it in parliament.”

Protests supporting the CJP movement were also held in Mumbai and Bengaluru, drawing hundreds of people.

Police stand guard at a sit-in protest calling for the resignation of Narendra Modi outside his residence in Delhi. Photograph: Arun Sankar/AFP/Getty

Modi has not yet directly commented on the protests, but the education minister Pradhan – who had dismissed the CJP protesters as a “b-team of terrorists” – took on a more conciliatory tone in his first comments since Monday’s protests.

In a social media post, he said: “We owe them [students] answers, reforms and accountability. That is exactly what our government remains committed to delivering,”

Allow Instagram content?

This article includes content provided by Instagram. We ask for your permission before anything is loaded, as they may be using cookies and other technologies. To view this content, click 'Allow and continue'.

The CJP’s founder, Abhijeet Dipke, urged protesters on Tuesday not to lose hope. “They want to break our spirit,” he said, from atop a lorry. “Do not let them silence you.”

Several key opposition parties, including Congress, have come out in support of the students’ movement and condemned the police violence against Monday’s protest.

Sandeep Dikshit, a senior leader of the Congress party, said: “What happened yesterday is our constitution got trampled upon. After that, no self-respecting politician or citizen can stand aside.”