A prominent Indian activist ended his hunger strike on Thursday after 26 days of fasting to demand the education minister’s resignation over a series of botched entrance exams. But India’s young protesters are continuing what has grown into a wider fight against corruption, poor job prospects and the government’s mismanagement of the education system.

The activist, Sonam Wangchuk, announced on social media that he had broken his fast “after long negotiations” with government ministers and “in view of possible violence in the country.” He had started striking in solidarity with a wider protest that began after India’s medical school entrance exams were canceled in May because test questions had been leaked.

The cause has since morphed into a wider Gen Z movement calling for structural changes to the education system and labor market, with thousands taking part in demonstrations in major Indian cities in recent days. In New Delhi, where the demonstrations began and have raged, and where young protesters were met on Monday by a heavy police response, anger against the government writ large has been intensifying.

The driving force behind the protests is the Cockroach Janta Party, a movement that is not a real political party and began as satire, taking its name from an insult. Its president, Abhijeet Dipke, said he was “relieved and grateful” that Mr. Wangchuk had ended his hunger strike. But he said the party’s peaceful protest would continue until the education minister resigns.

The party has called for nationwide rallies on Friday and said that protests had already spread to more than 30 Indian cities.

The Delhi police said its officers had moved Mr. Wangchuk, a longtime activist on education and climate issues, “to the hospital for essential medical care” in keeping with court orders. As Mr. Wangchuk’s health deteriorated there, government ministers urged him to break his fast.

Yet there was no indication that the government had agreed to meet any of the demands driving Mr. Wangchuk’s strike. Chief among them was the resignation of the Indian education minister, Dharmendra Pradhan, under whose watch a number of national exams have been marred by leaks. Mr. Wangchuck has also called on the government to vow not to punish protesters.

Mr. Wangchuck said he would offer an explanation for why he broke his fast in a video that would be published later. He urged “all to stay very vigilant about not allowing violence of any kind anywhere.”

Many of the protesters in India are students, and many others have jobs, but they share a sense of desperation and rage about education and employment prospects. As the movement spreads across the country, these young people are posing one of the most substantial challenges to Prime Minister Narendra Modi in his 12 years in power.