"The accused in the matter involved in the assault of a 20-year-old Johannesburg woman had made arrangements with police to hand herself over but she is yet to do so", Naidoo said.
Mugabe's immunity request is now under consideration, Clayson Monyela, a spokesman for the Department of International Relations and Cooperation told The Associated Press.
Discussions were taking place with Mrs Mugabe's lawyers and the Zimbabwean High Commission over the issue, it said.
Engels said she suffered deep cuts to her forehead and the back of her head, and on Monday, she registered a case with the police, alleging assault with intent to do grievous bodily harm.
Engels said she was in a hotel room with Mugabe's two adult sons when the attack took place.
Criminal attorney Riaan Louw said diplomatic immunity would not apply if Mugabe had indeed entered on private business.
"We don't know much about the new President Trump; some say he is impulsive, he does not think straight".
Fincham added: "They're no longer here".
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Following the Sunday incident, Grace Mugabe had agreed to appear in court on Tuesday but didn't show up, officials said.
"She flipped and just kept beating me with the plug". "I only found out this after I came out the hotel room. Because what happened to me was not OK".
The fact is that the SAPS should have done their job yesterday and arrested her as they would any other ordinary person who has a charge of assault against them.
The Zimbabwean president's wife, Grace Mugabe, has reportedly bought a multi-million pound house in Johannesburg amid an increasingly heated struggle over question marks over the successor to Robert Mugabe.
Received a PhD in September 2014, a month after being nominated to take over the leadership of the Zanu-PF women's league.
The 37th SADC Summit here in Pretoria will see Angolan president, Eduardo Dos Santos and Seretse Ian Khama present their farewell speeches as their terms are due to end this year.
His reign has been marked by brutal repression of dissent, mass emigration, vote rigging and a sharp economic decline since land reforms in 2000.