The violence has stirred public anger and galvanised India's opposition, posing a challenge for Prime Minister Narendra Modi's government.
Modi has not commented directly on the protests or engaged with the protesters, but on Thursday, he posted a statement on X that is being seen as an attempt to reach out to students who have been frustrated with repeated exam paper leaks.
"Nothing is more important than the welfare and future of our youth," he wrote.
"We have decided to set up fast-track courts to ensure swift and stringent punishment for those involved in paper leaks... This continues our series of steps for safeguarding the interests of students... Those who try to harm the future of our youth will not be spared."
A CJP spokesperson, however, said the real questions to be addressed were why paper leaks happen and who benefits from it.
"You are applying medicine after an injury, but our struggle asks why the injury has to happen," Ashutosh Ranka said in a video on X, indicating that the protesters would not back down until their demands were met.
While Wangchuk is not at the protest site any longer, many of the placards and posters have slogans about his fast and drawings of him.
Before being taken to hospital, he endured 21 days in Delhi's scorching summer heat on nothing but salt and water.
In a statement on Wednesday, Medanta Hospital, Gurugram, said the activist was admitted to the ICU.
"He is being treated by a multidisciplinary team of doctors. At present, he is stable, oriented, and his vital signs are within accepted parameters. All treatment being administered to him is in accordance with his informed consent."
On Wednesday, CJP founder Abhijeet Dipke, dozens of opposition MPs, activists and celebrities renewed their request to him to call off his hunger strike.
Health Minister JP Nadda, who had visited the activist at the hospital on Tuesday night, said he had also requested him to stop fasting.
"We inquired about his health and wellbeing. We also requested him to break his fast, join the mainstream, and guide the children in the right direction," he said, adding that the government was open to discuss the issues raised by Wangchuk.
But Wangchuk has refused all entreaties.