President Jacob Zuma’s son Duduzane should write affidavits instead of open letters, explaining why he had "robbed" South Africans of key assets, Save SA said on Tuesday.

"He should be preparing his submission to the commission of inquiry into State capture when it eventually happens. That is the 'letter' we are all waiting for, and which prompts us to ask, in the meantime: 'Duduzane Zuma, how do you sleep at night?'" Save SA said.

The organisation was responding to an open letter, purportedly written by Zuma, criticising former finance minister Pravin Gordhan.

The organisation described the letter as a "bizarre attempt to deflect attention away from the increasing evidence against him and his cronies of their central role in State capture and corruption".

Instead of explaining his role in State capture, Duduzane was resorting to "intimidation, incitements and hate speech".

On Monday, Gordhan told News24 that he would comment once he had read the letter and consulted his lawyers.

'State capture'

In March, President Zuma axed Gordhan and his deputy Mcebisi Jonas in a controversial Cabinet reshuffle.

Duduzane said that, during Gordhan’s tenure at Treasury, the economy had flat-lined, unemployment had risen from 21% to 27%, and the national debt had increased from 31% to a record 51% of the GDP.

He said Gordhan had used State bodies, such as the Financial Intelligence Centre and the SA Reserve Bank, to try and destroy him and his business colleagues, with no proof of misconduct.

"Yet you accuse us of State capture."

The president's son has numerous business interests which have direct and indirect links to the controversial Gupta family.

A series of emails leaked from the Gupta family indicate that Duduzane was at the helm of a media spin machine, together with British PR firm Bell Pottinger partner Victoria Geoghegan, to build a "long-term partnership" to "turn the tide of the country's trajectory".

In his open letter, Duduzane makes no mention about allegations of corruption involving the Guptas.

He claims that former Public Protector Thuli Madonsela’s "State of Capture" report was inconclusive and that the Hawks had found no wrongdoing involving him.

Zuma wrote that both he and the Guptas would welcome a judicial commission of inquiry into State capture.

They had exited their South African investments to protect jobs, he said.