Labour issues which led to a one-day strike on August 2 had not been resolved and the union would strike again on August 28, union spokesperson Kezia Lewins said.
"We want them to negotiate in good faith because we feel the prior round of negotiations were not in good faith."
The University of the Witwatersrand could not immediately be reached for comment.
Lewins said unions and management had not been in direct contact since talks broke down on the eve of the last one-day strike.
The two other unions, the Administration, Library and Technical Staff Association (Altsa) and National Education, Health and Allied Workers' Union (Nehawu), had joined in that strike.
Lewins said the two other unions would meet on Wednesday and likely vote to join the one-day strike.
The union was planning on pickets between 7am and 10am at the entrances of the university's main campus, as well as at the medical school, management and education campuses. This would be followed by a rally at noon on Main Campus.
Lewins said all three unions were working together and would only sign when all were prepared to accept management's offers.
"Because we're working as unions together, we'll only sign when all three of us are ready to sign," she said.
Asawu wanted better pay for academics and more money for research.
Support staff represented by Altsa and Nehawu also wanted higher wages, with the latter demanding a 9% increase.
The unions also had gripes about a lack of parking spaces and childcare facilities. – Sapa