Minorities' rights lobby group AfriForum, which is providing legal assistance to Ms Engels, has vowed to oppose any move by the government to grant Ms Mugabe diplomatic immunity.
The pretty model has lawyered up with Gerrie Nel, the prosecutor who secured a murder conviction against double amputee Olympic track star Oscar Pistorius.
It is unclear whether Grace Mugabe entered South Africa in a personal or an official capacity, which could impact her immunity appeal.
She said: "Whether one beats another ... it is wrong and the law must take its course ... but women are capable ... they can not be judged on that".
Engels claims Mugabe assaulted her with an extension cord at a Sandton hotel.
The other option would be for the South African government to delay making a decision on whether or not Mugabe will be granted diplomatic immunity, pending which she will be allowed to return home.
Chief executive Kallie Kriel said: 'The government has two responsibilities: one, to protect its own citizens and two, to act according to the law.
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South Africa's government is apparently anxious to avoid any diplomatic fallout from arresting the first lady of Zimbabwe, which has been led for almost four decades by Grace's husband Robert Mugabe, the 93-year-old president.
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They were told "let us talk and this can go away".
The Police Ministry says it will not be arresting Mugabe until it receives an official indication from Dirco.
The 52-year-old has been unable to leave South Africa since she arrived last week. They did so on the basis that she was part of the official Zimbabwean delegation to the SADC summit, even though it was clear she had been in South Africa on private business when the incident occurred, apparently for medical treatment.
South Africa's justice minister, Michael Masutha, told Reuters this week he was involved in discussions over the issue.
Mugabe is seen by many Africans as the continent's elder statesman and a hero of its anti-colonial struggles but Nelson Mandela accused him in 2008 of a "tragic failure of leadership" and Mugabe's relationship with President Jacob Zuma has been testy at times.
This isn't the first time Grace's temper has gotten her into trouble overseas, though usually nosey journalists are her preferred target.