A march in Durban on Friday is intended “to highlight the dangers of illegal skin-bleaching and stop.
"The withdrawal of the complaint... is worrying and disconcerting. Thus, we are extremely concerned that this case will result in an immense setback for our national fight against the rape epidemic in our country and the persistent harassment of women in the workplace," ANCWL deputy president Nosipho Dorothy Ntwanambi said.
Although the rape allegations had come to light via an internal grievance process, the Congress of SA Trade Unions might not be the most appropriate forum to properly investigate an allegation of rape, she said.
"Secondly, it was our view that Cosatu could not offer the comprehensive protection, support and assistance to the complainant, as it would be the case within the legal system," Ntwanambi said.
Vavi admitted having an extramarital affair with a married woman who worked for Cosatu. He claimed she later tried to extort R2 million from him. He denied raping her, and said the sex was consensual.
However, she brought a complaint of sexual harassment against him. The complaint was withdrawn during the internal grievance proceeding which started on Monday morning.
Vavi tweeted in the afternoon: "The complainant withdrew the 'grievance' after just 2hrs into the process. Thanks to so many who supported my family. Statement following."
The National Union of Metalworkers of SA (Numsa) said the allegations were part of a "dirty tricks" campaign by Vavi's opponents within Cosatu to destroy him.
"The timing of this claim is worrying and it reinforces our long-held view that a sinister campaign is being used to push Vavi out from his elected position for narrow political and selfish ends," Numsa said in a statement.
"We fully support Vavi during this difficult and testing period since he has not been found guilty by any court."
The SA Municipal Workers' Union (Samwu) said Vavi was being targeted because he had dared to speak truth to power.
"He [Vavi] has dared to speak the truth on unemployment, the absence of service delivery, corruption, and many other issues... and in so doing, has incurred the wrath of those with career ambitions," Samwu said in a statement.