Thousands of protesters gathered in New Delhi on Saturday to support a nascent Gen Z movement demanding more accountability in government, and specifically the resignation of India’s education minister, under whose watch there have been several scandals involving student exams.

The movement, called the Cockroach Janta Party, started as a joke after Abhijeet Dipke, a recent graduate of Boston University, created a satirical website in May for “lazy and unemployed” youth. He was responding to a remark by India’s chief justice, who compared jobless young Indians who criticize the authorities to cockroaches.

“How long will we live in fear of this government?” Mr. Dipke asked the crowd under a sweltering sun. He had come straight to the protest venue from the airport, after a long flight from Boston.

Mr. Dipke, 30, has become an accidental hero to millions of Indians — Gen Z and otherwise — who are frustrated with high youth unemployment, frequently mismanaged student exams and the sense that a heavy-handed government has eroded their democratic rights and ignored their interests.

“The future of this country is its youth,” said Shakeel Abdul, 35, an architect who had flown in from Bengaluru with a friend for the protest. “If we don’t give them support, then I would not call myself a citizen of this country,” he said.

In his speech, Mr. Dipke said his mother had been “very scared” that the government would arrest him when he landed. Until the last minute, it had been unclear whether the Delhi police would permit the demonstration, which was arranged at short notice.

The streets around the protest site were lined with police officers and paramilitary forces. But the event, which lasted about six hours, went off peacefully. Sonam Wangchuk, a well-known education and environmental activist who has long used civil disobedience, including fasting, as a means of protest, also spoke.

Many demonstrators were demanding the resignation of Dharmendra Pradhan, the education minister. His ministry oversees several national entrance tests, including a highly competitive one for entry into undergraduate medical school.

More than two million candidates took that test in early May, but soon afterward, the exam’s overseer said it had discovered that questions had been leaked. The education ministry canceled the test, meaning that everyone who took it would have to do so again or forget about medical school.

Students were even more angered by Chief Justice Surya Kant’s “cockroach” comment, which he made soon afterward in an unrelated case. Mr. Dipke’s satirical Cockroach Janta Party (“janta” means “the people” in Hindi) soon went viral, and then it morphed into a vehicle for the frustrations of millions of Indians.

“The government has neither jobs nor governance tools to improve education,” said Ram Sanehi, a 45-year-old teacher who found out about the protest on social media and traveled more than three hours to join it.

“I want to show solidarity with the Cockroach Janta Party as it is working toward the good of the country, if they truly mean what they say,” Mr. Sanehi said.

There was a steady flow of demonstrators at the protest site, even as temperatures exceeded 100 degrees Fahrenheit. People wore cockroach T-shirts and masks, and many carried placards calling for Mr. Pradhan to step down.

Mr. Pradhan has not addressed the demands for his resignation, but in interviews with news outlets, he has said that the government should not have allowed recent mistakes to occur. Another major exam, taken by many 12th-graders, was recently thrown into disarray when a newly adopted digital system botched the results.