Speaking to reporters in the city of East London, Manto Tshabalala-Msimang said she saw no reason to step down as long as she retained the backing of President Thabo Mbeki.
"I'm not. I'm not stepping down, because I don't understand why I should step down unless, as the president has said, you give him reasons for what it is that I have done," she was quoted as saying in the online edition of The Star newspaper.
"Have I neglected the duties assigned to me? Have I?"
A Sunday newspaper reported at the weekend that Tshabalala-Msimang, derided by critics at home and abroad as "Dr Beetroot" for touting vegetables to help combat AIDS, needed a liver transplant due to years of excessive drinking.
The Sunday Times also claimed she did not qualify for the transplant and was still drinking, damaging the new, donated organ.
It further reported the minister was convicted of stealing a patient's watch, hospital blankets, linen and heaters while a medical superintendent at a hospital in neighbouring Botswana in the mid 1970s, and was subsequently declared a prohibited immigrant.
Cabinet members denounced the reports as "distasteful" but did not deny any of the accusations, while insisting on Tshabalala-Msimang's right to privacy.
"The sacrosanct principle of doctor-patient confidentiality must be respected at all times," government spokesman Themba Maseko told journalists in Cape Town.
Maseko said the cabinet felt it was "inappropriate" to discuss the published allegations against the minister, saying Mbeki would consider any information brought to his attention.
The appointment and dismissal of minister's was Mbeki's prerogative, he added, with no explanation required.
The cabinet supported Tshabalala-Msimang's intention to take the newspaper to court as "a legitimate way of ensuring that clear parameters are set on the balance between the rights to privacy and to dignity, especially their application to public figures, and free speech."
And it accused the Sunday Times of basing its stories on the "unlawful publication and theft of her medical records from the hospital".
South Africa's main opposition Democratic Alliance has demanded the sacking of the minister, who has been under fire in recent years over her perceived apathy to the country's AIDS pandemic.
Maseko rejected as "spurious and irresponsible" assertions that Mbeki had enabled the minister's liver transplant, and warned that the office of the president was due "a level of respect".