At least 10,000 joined the protest, triggered by a police raid on a student dormitory last Friday which resulted in three reported deaths, 20 students being taken to hospital and about 1,000 arrests.
At the same time, university deans and other academic staff announced a sit-in on the campus today as a gesture of "hatred towards the tragic and bloody incident" of last Friday. The university's chancellor resigned in protest against the police actions.
The demonstrations are seen as the biggest test of government authority since the 1979 revolution, which brought down the monarchy. They take place against a backdrop of worsening tension between the country's reformist president, Mohammad Khatami, and Islamic hardliners loyal to the country's religious leader, Ayatollah Ali Khamenei.
Making clear his own sympathies for the students, President Khatami expressed "deep regret" over the raid on the university, calling it an "ugly and bitter incident".
Students turned on police cars that tried to block their way to the city centre. "I am going to kill my brothers' murderers," they chanted. "Either Islam and the law, or another revolution." Drivers caught up in the protest sounded their horns in support of the students, while local residents offered them iced water to counter the summer heat.
Although the students shouted slogans in support of the embattled Iranian president, he may feel embarrassed by their demands for him to directly confront the religious establishment. The students' principal demands are for the return to the news-stands of a banned pro-Khatami newspaper, Salam, the abolition of press censorship laws adopted by the hardline parliament last week, and an end to panels of clerics vetting election candidates.
They also want the removal and punishment of the police chief, Hedayat Lotfian, an ally of Ayatollah Khamenei.
A session of the National Security Council chaired by the president on Saturday night promised to investigate the raid and sack the police official who ordered the assault, but made no mention of sacking the police chief.
In a sign that protests may be spreading across the country, students were reported to be holding sit-ins and protests in the university cities of Mashhad and Isfahan.
About 1,000 students also rallied in the northern city of Rasht, and demonstrators gathered in the north-western city of Tabriz.
Most worryingly for the Ayatollah, there were reports from the holy city of Qom that clergy had also come out in support of the students, closing lectures in protest against the events in Tehran university.
Iranian journalists said they would go on strike tomorrow to protest against the closure of Salam. The strike would in effect close down all the main national dailies.