President Jacob Zuma's son Edward has read former Public Protector Thuli Madonsela the riot act, saying she "should either become a full-time politician or just shut up".

It appears as though Madonsela's comments on her preferred candidate to succeed his father have riled the president's eldest son.

"It is either she decides to be a politician full time or just shut up," a livid Zuma said, responding to Madonsela's statements made during a Cape Town Press Club function on Monday.

During the event Madonsela, who left office of the Public Protector in October and was currently on a fellowship at Harvard University, was asked if she would consider becoming the next president.

"I am neither qualified to be president nor interested in that job," she said.

Madonsela went on to say that South Africa deserved a good president.

'Insult' to Nkosazana Dlamini-Zuma

She said she hoped that the next president would be one that built a united South Africa.

"Should he be a male, should she be a female...I would love it to be a female but I would hate to have a female that is a proxy, because that would be worse than having a man," Madonsela said.

An irate Zuma said: "She is rude. She would love to see a female South African president but it should not be a proxy, clearly she is insulting uNkosazana [Dlamini-Zuma]."

Zuma said he was offended by Madonsela's remarks.

"She was addressing a white dominated gathering in Cape Town, she is a proxy herself."

He said it was well known that Dlamini-Zuma was the preferred female candidate to succeed Zuma. If Dlamini-Zuma, who had the support of the ANC Women's League, were to succeed in her candidacy, she would likely go head-to-head with Deputy President Cyril Ramaphosa for the top position. However, the party has yet to officially open the succession debate.

Current Public Protector 'undermined'

"My interest is the ANC, clearly the female candidate is known, it is Nkosazana, we all know that. Obviously if she says she does not want a president who is a proxy, she is referring to her, whose proxy is Nkosazana?"

He questioned the CX report that Madonsela touched on during the briefing.

"That investigation is still in the office of the Public Protector, Advocate Busisiwe Mkhwebane. She is basically undermining Busisiwe, the current Public Protector."

Zuma wondered who Madonsela was trying to impress.

Madonsela could not be reached for comment after repeated attempts.