"We have no interest in repeating the ANC's clarifications on the wild allegations published in the media, which Ms Mazibuko parroted in her letter," Mathole Motshekga said on Wednesday.
"We therefore hope that the president will ignore her nonsensical letter with the contempt it deserves."
On Wednesday, Mazibuko wrote an open letter to Zuma calling on him to "demonstrate the leadership" required of him.
"He must immediately put a stop to the ANC's campaign to discourage investment and destroy jobs through aggressive and irresponsible language and conduct," the letter read.
"While Mr Zuma is busy selling South Africa as an investor-friendly market at the World Economic Forum in Switzerland, his actions back home, and those of the party he leads, are working towards the opposite goal."
Motshekga said the letter contained "wild and spurious accusations that cannot be substantiated", making the letter "extremely difficult to take seriously".
The open letter
In the open letter Mazibuko touches on a number of issues ranging from the challenges facing the mining sector to the upgrade of ministerial homes, a recent advertising campaign by FNB and Zuma's failure to take action on these issues.
The FNB campaign features a number of videos of children in school uniform reading their hopes for the country.
Last week, Anglo American Platinum announced its plan to stop production at four of its shafts – Khuseleka One and Two, and Khomanani One and Two, in Rustenburg – which could result in the loss of 14 000 jobs.
On Monday, the public works department confirmed that it spent R65-million on renovating ministers' houses.
Mazibuko said Zuma should live up to the name given to him by ANC deputy president Cyril Ramaphosa as the "action man".
Zuma's 'time to act is now'
"As president of the republic and leader of the governing party, Mr Zuma has the power and responsibility ... to take decisive action where necessary, to instil real confidence in the stability of our nation," she said.
"If he is truly South Africa's 'action man', and is serious about attracting investment to South Africa, then the time to act is now."
"Rather than being outraged at Impala Platinum's unilateral action to send more people to the unemployment queue, Ms Mazibuko directs her criticism at those who are tirelessly working to ensure sanity prevails and thousands of jobs are saved," Motshekga said.
"The defence of the FNB by Ms Mazibuko is also unsurprising, given the striking similarities between the DA's political rhetoric and the bank's latest political campaign."
He said insults did not build a climate for constructive, frank and open public discourse but diminishes it.
"Insults polarise our society, poison social relations and derail the progress the nation has made," he added.
"The modus operandi of propagating defamatory claims, untested and unsubstantiated allegations is what makes it difficult for us to distinguish between this banking institution and the DA." – Sapa.