South Africa’s student movement has scored a big victory after plans to raise university fees were scrapped following weeks of nationwide protests that culminated in a mass gathering outside the main government offices.

The largest demonstration took place at the Union Buildings, South Africa’s seat of government in Pretoria. More than 10,000 people gathered on Friday to demand that proposed fee rises be scrapped, and called for the president, Jacob Zuma, to personally address their concerns.

It was the largest single student protest since the 1976 Soweto uprising – an iconic moment in the fight against South Africa’s apartheid regime – and participants represented a broad cross-section of the country’s racial groups and political parties.

Although the presidential podium was erected twice, Zuma never appeared, choosing instead to make the announcement in the press room inside the main building.

“We agreed that there will be a zero increase of university fees in 2016,” he said after a meeting with student leaders. Universities had proposed fee rises of up to 11.5% next year, arguing they need higher fees to keep up standards.

Zuma’s non-appearance infuriated protesters. A small minority tore up security fences, burned portable toilets and threw rocks at police. The police responded forcefully, using teargas, rubber bullets and stun grenades to disperse the crowd. Running battles between small groups of protesters and police continued after sunset, damaging several vehicles.

“It’s wrong. We were invited here by the president, and we’ve been waiting all day. We had to react. We had to show the president this is serious,” said Tobago Madiba, 21, a student from the Tshwane University of Technology, his eyes closed after exposure to teargas.

The demonstration had begun peacefully, with protesters chanting and holding up signs with slogans. When some protesters began to throw rocks, others tried to dissuade them by chanting “Non-violence! Non-violence!”

Protesters in Pretoria on Friday. Photograph: Siphiwe Sibeko/Reuters

Student leader Mcebo Dlamini, a key organiser at the University of Witwatersrand, said students had not caused any violence. “There is no violence here. We have seen students reacting to the brutal system of the ANC [the ruling party].”

Stephen Grootes, a political commentator, said the success of the student protests posed a headache for the ANC. “What this does reveal is the ANC’s inability to deal with a multiracial, multiclass and multiparty group of people who refuse to buy into the old political narrative,” he said.

There were protests in most big city centres throughout the country. Hundreds of South African and international students also attended a solidarity rally outside the South African high commission in London.

It is unclear whether the students will put their placards away and return to class on Monday. Many were angered by the forceful nature of the police response, while others were determined to use this momentum to push for the scrapping of university fees altogether. “Now we know Zuma is a coward. He’s not a man. We want more now, not just a 0% increase. We want free education,” said Ngavatshedzo Mpepu, 24, from the University of Pretoria.