India’s education minister stepped down on Saturday, in a major victory for a student protest movement whose explosive rise has become one of the most serious challenges in years to the power of India’s prime minister, Narendra Modi.

The education minister, Dharmendra Pradhan, submitted his resignation to Mr. Modi, bowing to weeks of public pressure that culminated in nationwide street protests from Delhi and Mumbai to Kolkata and Chennai.

The movement emerged in May, powered by widespread anger and frustration after the government ordered millions of students to retake a national medical school entrance exam because test questions were leaked. Students held Mr. Pradhan, under whose watch a number of national exams have been marred by leaks, directly responsible.

At the forefront of the protests is the self-described Cockroach Janta Party, which takes its name from an disparaging remark (by the Chief Justice of India) and has made Mr. Pradhan’s resignation a central demand. The group began protesting in June, but the movement gained momentum this month, after the police cracked down with force on demonstrators who marched on Parliament in New Delhi. Protests have spread to major cities across India.

Mr. Pradhan was previously largely dismissive of the protests. In a social media post he accused opposition parties of exploiting students to “manufacture disruption,” and in a June interview with a local media outlet referred to the student protesters as “the B-team of terrorists.” But that appeared only to strengthen the resolve of the students to remove him. Despite winning some rare concessions from the government, they vowed to continue the protests until the minister was dismissed.

The call to remove Mr. Pradhan has forced Mr. Modi to balance loyalty to his supporters against the need to placate young people, who account for 40 percent of India’s population. An operative of the ruling Bharatiya Janata Party, Mr. Pradhan was credited with helping the B.J.P. come to power in some recent state elections. Over a nearly three-decade political career, he has held various positions in the party.

But the exam leak scandal in May triggered long-simmering frustrations about government accountability and a lack of jobs and opportunity that Mr. Modi cannot immediately address. India puts students through a pressure-cooker education system, and yet nearly 40 percent of graduates between the ages of 15 and 25 are unemployed, according to a 2026 study. Student suicides are increasing faster than those of the overall population.

The students’ victory could motivate them to push their demands further. Aside from education, the Cockroach Janta Party is also asking the government to consider its far more sweeping agenda for change, including judicial reforms, gender quotas for Parliament and punishments for politicians who defect from their political parties after being elected.