Athletics world governing body the IAAF is still analysing the results of Semenya's tests and wants to discuss them with the athlete.
It has indicated that she is unlikely to be asked to return the gold medal she won in Berlin, but questions remain over her future in women's sport.
Asked what would happen if she was barred from competition, Stofile said: "I think it would be the third world war.
"We (would) go to the highest levels in contesting such a decision. I think it would be totally unfair and totally unjust.
"Neither Caster nor her family deserves this humiliation. None of them have done anything wrong. And we appeal that they be left alone.
"We have referred the matter to our lawyers to see how best her rights and interests can be protected."
Stofile was speaking after media reports in Australia claimed a source had revealed that Semenya's test results showed her to be a hermaphrodite - someone who has some or all of the primary sex characteristics of both men and women.
But South Africa's athletics president Leonard Chuene told the Star newspaper: "The IAAF told us this week that the tests are inconclusive and they could not give us the results just yet.
"So I really do not know where the Australia media got this latest one from."
National Assembly's sports committee chairman Butana Komphela added: "Someone is guilty of leaking her confidential medical information to Australian newspapers."
However, IAAF spokesman Nick Davies said: "The statements should be treated with caution as they are not official statements by the IAAF.
"We have received the results from Germany, but they now need to be examined by a group of experts and we will not be in a position to speak to the athlete about them for at least a few weeks.
"After that, depending on the results, we will meet privately with the athlete to discuss further action."
The IAAF has confirmed it will not comment further on Semenya until after the IAAF council meeting in Monaco on 20-21 November.
BBC sports news correspondent Gordon Farquhar said: "It's likely that she has some hermaphroditic or intersex condition.
"We already know that she has testosterone levels that are three times higher than those normally expected in a female.
"It's a serious issue and the athlete has to be told the implications.
"There are three possible outcomes from the expert's discussions: that the condition does not give her a competitive advantage; the condition gives her a competitive advantage, which cannot be treated; or most likely, the condition can be treated in some way if she consents to it, and in time she can return to competition."
"The IAAF has to weigh the interest of the athlete, an apparently innocent victim in this, with its responsibility to ensure fair competition."
Semenya won the 800m title in Berlin in August in the fastest time of the year, one minute, 55.45 seconds, 2.5 seconds ahead of Kenya's 2007 champion Janeth Jepkosgei.
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