"Sadtu has not received any apology and has no business in receiving one because the misconduct was subject to internal procedures in Cosatu," the teachers' union said on Monday.
"We reject, with the contempt it deserves, this misleading information aimed at bringing internal divisions within the union."
On Friday, the SABC reported that Sadtu had come out in strong support of the Cosatu' general secretary at a meeting in Port Elizabeth.
This followed Vavi admitting to an extra-marital affair with a married junior employee at Cosatu and allegations of rape. The woman withdrew her sexual harassment grievance against him.
Vavi was reportedly loudly applauded by Sadtu members during a speech in which he apologised for embarrassing the trade union federation.
Rule of law
​Sadtu said it believed in the rule of law and constitution of Cosatu.
"We have afforded the leadership of our federation an opportunity to deal with this operational issue by following procedures to deal with the misconduct and avoided to deal with this matter in the media," the union said.
"This is a principled position of our union [which] is to respect internal processes and procedures."
It was reported on Sunday that Vavi would face a disciplinary hearing for bringing Cosatu into disrepute, after he admitted to having the affair.
Cosatu's regular top officials meeting, which would be held on Monday, would reportedly call for a special sitting of the central executive committee to initiate disciplinary charges against Vavi.
Cosatu spokesperson Patrick Craven on Sunday said the trade union federation was not commenting on the matter. – Sapa