"Comrade Asvat was a personal friend, a family doctor and a man of deep compassion," she told reporters in Johannesburg.
"He sought me out in Brandfort (where she was once restricted) at the risk of torture and imprisonment."
Madikizela-Mandela said any journalist or editor worth anything would investigate the veracity of assertions by murderers who did not even apply for amnesty before the Truth and Reconciliation Commission.
The African National Congress Women's League president said she complained to National Police Commissioner George Fivaz in 1995 about Cyril Mbatha and Thulani Nicholas Dhlamini being tortured by the police to implicate her in the murder of Dr Asvat.
The media in 1995 quoted Fivaz as saying: "The allegations were so serious that they demanded immediate clarification, in the interest of Mrs (Winnie) Mandela and the police - the allegations, if true, would constitute a serious blot on the police and a grave infringement of Mrs Mandela's personal rights."
"It is 1997 and I ask what has become of this investigation," said Madikizedla-Mandela.
She challenged Katiza Cebekhulu, a member of the former Mandela United soccer team who has accused her of hiring Asvat's murderers, to come back to South Africa to stand trial for the murder of teenage activist Stompie Seipei.
Cebekhulu, who was one of Madikizela-Mandela's co-accused in her kidnap and assault trial relating to the disappearance of Seipei and the assault of three other youths, has also accused her of killing Seipei.
"He must... say who helped him leave the country and why," Madikizela-Mandela said, referring to Cebekhulu's disappearance shortly after the kidnap trial started in 1992.
She asked whether the state machinery was unable to get hold of Cebekulu, whom she described as "the unsophisticated person".
Madikizela-Mandela, a member of the ANC's national executive committee, said it was not enough to have foreign parliamentarians come and testify before the TRC on issues that they had no factual knowledge of.
"South Africa demands more," she said. "If it is in search for the truth, why are we unable to get to the truth - so that my right to fair treatment can be asserted."
Madikizela-Mandela said she had been watching in painful silence her character being butchered in the media, and she had also witnessed her contribution to South Africa's democracy being vilified and ridiculed.
"I have seen confused panic in my grandchildren's tearful eyes, attenmpting to work out whether I am the demon I am portrayed."
"When will I enjoy the respect that is accorded everyone?," she asked.
Madikizela-Mandela repeated her intention to testify before the TRC, and said again it should be done in public.
"I beg that these issues be tested by the vigilance of the public. Let this serve as a public spectacle of the last kind. Let me claim the right to decent treatment once and for all."
Journalists were not allowed to ask her further questions.
Former member of the SA security branch Paul Erasmus, who flanked Madikizela-Mandela at her press conference at the ANC's Shell House headquarters, on Tuesday repeated claims of a National Party government campaign to discredit the ANC, especially Madikizela-mandela.
He said he had heard that Seipei was killed by Richardson, whom the youth activist had threatened to expose as working for the security branch.
Mpumalanga premier Mathews Phosa echoed Madikizela-Mandela's sentiments that the TRC was the best forum for discussing allegations on the Asvat and Seipei murders.
"Let's subject ourselves to the TRC," said Phosa.
The group with Madikizela-Mandela, including her lawyers, would not comment on the book Katiza's Journey, based on Cebekhulu, saying they had not seen it or read it.