The US leader has supported protesters in the past – at one stage appearing to encourage them with a promise that “help is on its way”.
Footage verified by the BBC shows hundreds of protesters – many with national Iranian flags – peacefully marching on the campus of the Sharif University of Technology at the start of a new semester on Saturday.
The crowds chanted “death to the dictator” – a reference to Supreme Leader Ayatollah Ali Khamenei – and other anti-government slogans.
Supporters of a rival pro-government rally are seen nearby in the video. Scuffles are later seen breaking out between the two camps.
Verified photos have also emerged showing a peaceful sit-in protest at the capital’s Shahid Beheshti University.
The BBC have also verified footage from another Tehran university, Amir Kabir University of Technology, showing chanting against the government.
In Mashhad, Iran’s second-largest city in the north-east, local students reportedly chanted: “Freedom, freedom” and “Students, shout, shout for your rights”.
Sizeable demonstrations in other locations were also reported later in the day, with calls for further rallies on Sunday.
It is not immediately clear whether any demonstrators have been arrested.
Last month’s protests began over economic grievances and soon spread to become the largest since the 1979 Islamic Revolution.
The US-based Human Rights Activists News Agency (Hrana) said it had confirmed the killing of at least 6,159 people during that wave, including 5,804 protesters, 92 children and 214 people affiliated with the government.
Hrana also said it was investigating 17,000 more reported deaths.
Iranian authorities said late last month that more than 3,100 people had been killed – but that the majority were security personnel or bystanders attacked by “rioters”.