"The honeymoon is over," a student leader said, handing out the group's conditions outside the ANC's Luthuli House in Johannesburg.
Students' demands include scrapping fee increases set to take effect next year. Initially fees were to be raised 10%, but the South African government later dropped that hike to 6%.
CNN's David McKenzie reported the students who gathered Thursday refused to let the ANC's secretary-general speak. Protest leaders called for a march Friday on the Union Buildings,
the official seat of South Africa's government in Pretoria, he said.
South African President Jacob Zuma plans to meet Friday with student leaders and university administrators, his spokesman, Bongani Majola, said earlier.
Students storm Parliament
Student protests have raged since Monday, with demonstrators barricading entrances to South African campuses, including the University of Cape Town and University of the Witwatersrand in Johannesburg.
More than a dozen universities are shut down because of the protests. Students are using the hashtag #FeesMustFall to rally and share experiences on social media.
On Wednesday, throngs of students left the University of Cape Town and stormed the South African Parliament.
Students pushed past guards and forced open the gates. Once inside parliamentary grounds, they sat in front of the building to block Parliament leaders from getting out.
"The group of protesters was massive," said Jabulile Newman, 21, a university junior who attended the demonstrations.
Police "started throwing grenades and firing tear gas," Newman said.
Aziz Matthews, 23, a university senior, said, "The protest was peaceful, but we were met with violence from the police.
"We had our hands raised to show we weren't a threat and sat down many times to listen to speeches."
Police: 6 students arrested in 'illegal protest'
The South African Police Service
said Thursday that six students had been arrested during what it called the "illegal protest" and were being detained at a Cape Town police station.
"They will appear before the Cape Town Magistrate's Court on Thursday, facing charges of Trespassing and Contravening the Gatherings Act," a police statement said.
Earlier, police said departments and security forces were helping take "a multidisciplinary approach" to address the protests following Wednesday's incident.
"The behavior of those students is unacceptable and should not be condoned in any way," the statement said.
It did not address accusations that police used tear gas on students. CNN could not reach police officials by phone.
The United States said it was monitoring the situation in South Africa.
"We've seen the reports (of clashes), obviously concerned by them," said John Kirby, a State Department spokesman. "We're looking into it and monitoring it closely. Obviously, our position ... of the right of peaceful protest remains the same."