They have been the biggest student protests to hit South Africa since apartheid ended in 1994.
The students had rejected an earlier government offer to cap increases at 6%, down from the 10% to 12% proposed by the management of universities.
President Jacob Zuma announced the move as students gathered by his office in Pretoria.
Before Jacob Zuma’s TV address, police had been firing stun grenades and using water cannon to stop a small group of students breaking into the Union Building, the seat of government in Pretoria.
On October 21, police clashed with students trying to force their way into the parliamentary complex in Cape Town.
The demonstrations have closed some of South Africa’s top universities.
“We agreed that there will be a zero increase of university fees in 2016,” Jacob Zuma said after meeting university officials and student representatives.
“In the long term, there is a package of issues that was raised at the meeting that needs to be followed up – these include free education, institutional autonomy [and] racism.”
During the protests, universities said they needed to increase fees to maintain standards, as they had been hit by a fall in government subsidies.
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