Athletics' governing body declined to confirm the report in Australia's Daily Telegraph newspaper, which said the 18-year-old runner had both male and female sexual characteristics.
The IAAF said medical experts are examining the results of gender tests on Semenya, who won the women's 800 metres at last month's World Championships in Berlin. No decision would be taken until late November.
"I think it would be the third world war. We will go to the highest levels in contesting such a decision. I think it would be totally unfair and totally unjust," said Sports Minister Makhenkesi Stofile.
South African President Jacob Zuma decried the invasion of Semenya's privacy and what he called the violation of her rights, although neither he nor Stofile denied the report.
"I don't know why we should not respect the privilege between the doctor and the patient. Why, when the tests have been done, why was it published?" Zuma said.
The Telegraph report said tests had found Semenya had no womb or ovaries, but that she had internal testes, the male sexual organs which produce testosterone, and her levels of the hormone were three times that of a 'normal' female.
It said the IAAF was "ready to disqualify Semenya from future events and advise her to have immediate surgery because her condition carries grave health risks. They have also not ruled out stripping Semenya of her 800m world championships gold medal."
'SHOCK AND DISGUST'
Semenya, who was due to compete in a cross country race in Pretoria on Saturday, in her first competition since claiming the world title, withdrew from the event. Semenya's coach Michael Seme said that she is not "feeling well."
Stofile told a news conference his ministry had "noted with shock and disgust" media reports on the test results, which the South African government had not yet received.
"The issue here is that this girl has undesirable levels of testosterone -- what does it matter? That is neither here not there. She does not have a womb -- so what?," he said.
Nick Davies, spokesman for the International Association of Athletics Federations (IAAF), said media reports on the gender test results should not be considered as official statements by the sports body.
"There is a (IAAF) Council on 21 November and this will be the opportunity to conclusively finalise a decision," he said.
Some South Africans have accused the IAAF of racism for ordering the gender tests on Semenya, saying her broad shoulders and imposing musculature are common in women's athletics.
The controversy may have touched a raw nerve in a country where race is still a highly sensitive issue after decades of apartheid, which ended in 1994.
The militant Youth League of South Africa's ruling African National Congress (ANC) said in a statement: "Even if a test is done, the ANC YL will never accept the categorisation of Caster Semenya as a hermaphrodite, because in South Africa and the entire world of sanity, such does not exist."
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