The South African Union of Students (SAUS) said that the decision was taken following a meeting with Higher Education Minster Blade Nzimande earlier this week.
Students said that they were not willing to back down and would be taking their fight for free higher education to the Union Buildings at a date yet to be announced.
The minister said that the 2021 academic year was already shorter than usual, having started later, due to lockdown delaying the conclusion of the 2020 academic year.
The situation remains tense, with police chasing protesting students through the streets of Braamfontein.
The threats come after days of protests at various universities across the country last week.
This after the SAUS met Deputy Higher Education Minister Buti Manamela in Pretoria on Saturday to discuss a memorandum of demands.
The SA Union of Students gave Higher Education Minister Blade Ndzimande until 5pm on Friday to respond to the list of 15 demands which included the scrapping of historical debt.
Institutions opened their doors to 33% of their student population, mainly those in their final year and those studying medicine who've been on the frontline across government hospitals.
CEO Ahmed Bawa said reducing tuition fees would affect the ability of universities to pay staff, which will be disastrous for the sector.
The union on Monday said student fees partly account for contact classes, which haven't fully taken place because of the lockdown.
Students at the institution have been staging protests since last week, demanding that they be allowed to register without settling their historical debt.
This as students in KwaZulu-Natal and the North West this week launched protests focusing on several grievances, including fees and student debt.
Student protests flared up across the country this week with calls for a national shutdown at public universities.
There were protests at the Durban University of Technology and the University of KwaZulu-Natal on Monday over a number of matters.
Higher Education Minister Naledi Pandor says the turnaround at NSFAS has ensured that 2019 students benefiting from financial aid scheme are already receiving allowances.
Higher Education Minister Naledi Pandor convened a one-day meeting in Boksburg to discuss advancing transformation in the sector on Monday.
The union says Dlamini is a social activist and was fighting for a genuine course of free education.
In July, Higher Education Minister Naledi Pandor revealed the extent of the damage caused during the 2016 protests had soared to nearly R800 million.
