Students were detained by Delhi police on Wednesday as they gathered to watch a recent BBC documentary about Prime Minister Narendra Modi.
The Indian government has dismissed the documentary as propaganda and blocked its streaming and sharing on social media.
This follows similar disruptions, some of which turned violent, at gatherings this week by students to watch the documentary that questions Mr Modi's leadership during deadly riots two decades ago.
His opponents are also raising questions of government censorship.
Mr Modi, who is aiming for a third term in elections next year, was chief minister of Gujarat in February 2002 when a suspected Muslim mob set fire to a train carrying Hindu pilgrims, setting off one of independent India's worst religious bloodsheds.
In reprisal attacks across the state, at least 1,000 people were killed, mostly Muslims, as crowds roamed the streets over days, targeting the minority group. Activists put the toll at around 2,500.
Mr Modi has denied accusations that he did not do enough to stop the riots, and he was exonerated in 2012 following an inquiry overseen by the Supreme Court.
A petition questioning his exoneration was dismissed last year.
The government has said the BBC documentary India: The Modi Question, released last week, is a biased "propaganda piece" and has blocked the sharing of any clips from it on social media.
The Students' Federation of India (SFI) said on Wednesday that it planned to show the documentary in every Indian state. SFI is the student wing of the Communist Party of India (Marxist).
"They won't stop the voice of dissent," said SFI general secretary Mayukh Biswas.
Ahead of one of the screenings at Delhi's Jamia Millia Islamia university, 13 students were detained amid a heavy police deployment.
The university blamed the students for creating a "ruckus on the street" and said they did not have permission to screen the show, police said.
"There is no chance that anybody who tries to disturb the discipline of the university will go free," the university's vice chancellor Najma Akhtar told Reuters.
A day earlier, bricks were hurled, allegedly by members of a right-wing group, at students hoping to watch the documentary at Delhi's Jawaharlal Nehru University, students said.
Student leader Aishe Ghosh said they were watching the documentary on their phones and laptops after power was cut off about 30 minutes before a scheduled screening. The university had denied permission and threatened disciplinary action if the documentary were screened.
"It was obviously the administration that cut off the power. We are encouraging campuses across the country to hold screenings as an act of resistance against this censorship," said Ms Ghosh.
The media coordinator for the university did not comment when asked about the on-campus power cut.
The SFI spokesman did not respond to a message seeking comment nor did the police spokesman respond to queries.
Protests also erupted following the film's screening at campuses in Kerala on Tuesday, while a show was cancelled mid-way at a university in Chandigarh, according to local media reports.
Mr Derek O'Brien, a member of parliament in the upper house, tweeted on Saturday that the opposition "will continue to fight the good fight against censorship" in reference to the ban on sharing clips from the documentary on social media.
"The documentary was rigorously researched according to highest editorial standards," the BBC said. It approached "a wide range of voices, witnesses and experts" and featured a range of opinion including responses from people in Mr Modi's Bharatiya Janata Party.