The months-old movement and the protest are seen as the biggest public challenge to Prime Minister Narendra Modi in his third term in office, drawing millions of supporters on social media before broadening its appeal to opposition parties.
A police decision to forcibly move hunger-striking activist Sonam Wangchuk to hospital on Saturday has galvanised a movement seeking the resignation of Education Minister Dharmendra Pradhan for exam paper leaks.
Thousands of young supporters arrived through the night at the protest site of Jantar Mantar in New Delhi for the march on the opening day of parliament's monsoon session.
"The government had reached out for talks in the morning. Our demands are clear," Saurav Das, CJP chief spokesperson, said in a post on X while on his way with another CJP member to meet Health Minister JP Nadda for the talks.
Nadda is the previous president of Modi's Bharatiya Janata Party. Scores of police and paramilitary security personnel were seen across the capital, stopping protesters as they chanted slogans holding the national flag.
"The protest site has already run out of space and this can lead to an untoward situation," Sachin Sharma, Delhi's deputy commissioner of police, told Reuters, adding that there were more than 10,000 protesters on Monday morning.
Reuters reporters saw scores of young people walking towards the protest site from metro stations as police barricaded multiple routes to central Delhi, causing major traffic jams and diversions.
Government offices in the parliament area were locked to prevent protesters entering.
Television visuals showed police caning some protesters in a heavily barricaded area, although Delhi Police denied any use of force and said the "protest is being handled professionally".
The CJP also said some protesters had reported tear gas being fired to disperse them near parliament.
Reuters journalists in the area also heard sounds of blasts but could not see rounds being fired from their locations.
"Quit, quit," the protesters chanted.
"Dharmendra Pradhan quit", "Narendra Modi quit", they chanted in Hindi referring to the education minister as well as the prime minister.
The CJP movement began after national medical school entrance test papers were leaked in May, affecting more than two million students as it forced them to sit the test a second time.
CJP founder Abhijeet Dipke and his supporters began a sit-in in June seeking the resignation of Pradhan.
Wangchuk joined them on June 28, launching an indefinite hunger strike at the site. Wangchuk, in a handwritten note, requested the hospital to permit him to join the march, even if temporarily.
Earlier on Monday, he offered to end his hunger strike if the government agreed to three conditions including taking responsibility for what he said were recent failures in the education system and for the exam leaks.
He said he would also end his action if lawmakers and leaders of various parties met him in hospital and assured him the conditions would be met.
The rise of the CJP reflects frustrations among young Indians over issues like high youth unemployment and frequent examination paper leaks, analysts say.
