Police have put out a red alert to stop Zimbabwe's first lady Grace Mugabe, who is accused of assault, from leaving South Africa.
She is alleged to have assaulted a 20-year-old model who was in a hotel room with her two sons in Johannesburg.
Gabriella Engels claims she was beaten with an extension cord and posted a picture on Twitter showing a gash on her forehead.
She said the first lady's bodyguards had stood by watching.
Her lawyers claim she has received an offer of money to make the case "go away".
Mrs Mugabe, 52, has requested diplomatic immunity over the alleged incident.
The country's police minister said she is still in South Africa but that all border posts had been told to stop her leaving.
"The SAPS (South Africa Police Service) have already put tabs in the borders in relation to her leaving the country... The red alert has been put," said Fikile Mbalula.
Ms Engels appeared at a press conference on Thursday with several large white dressings on her head and a large photo of her injury and Mrs Mugabe in the background.
Gerrie Nel - the prosecutor seen by millions around the world in the Oscar Pistorius case - spoke to the media.
He said Ms Engels was suffering "secondary trauma" from all the attention.
"The family's even been approached by a third party to accept an amount of money to settle this," Mr Nel claimed.
He said no amount had been mentioned - "just an offer - 'let us talk and this can go away'."
'Equal before the law'
The lawyer said it was important that everyone is "equal before the law" and that if the state did not take action they would consider taking the matter to court privately.
"From our point of view," said Mr Nel, "We would expect at least a trial or action withing three months."
He said Ms Engels had been phoned on Thursday morning by the investigating officer, who told her police will now apply for a warrant for Mrs Mugabe's arrest.
Ms Engels' representatives also said they had sent a letter to the government over a convention that diplomatic immunity "cannot be used to escape prosecution from grave crimes".
The alleged victim, who sat alongside her mother, did not speak to reporters.
Her representatives said it was in case she had to testify in a trial.
They said there had been no threat made to Ms Engels - but that "she is living in fear of going out in public now, the family's living in fear for what might happen".
Robert Mugabe, 94, and his entourage flew into a South African country late on Wednesday - apparently arriving early for a regional summit of African leaders.