City Press reported that R203-million of state funds would be spent on the upgrade, with Zuma paying only 5% of the bill – around R10-million.
Speaking for the first time after Sunday's exposé, Nxesi defended the expenditure, but refused to confirm the amount of state funds spent on the project.
He slammed City Press for publishing details from "top secret" documentation.
"The merely unlawful possession of a top secret [document] is a breach of the laws … This therefore calls for an investigation to be launched to determine how the City Press illegally ended up in possession of this document," Nxesi said.
Nxesi defended the expenditure, saying it was in line with the Ministerial Handbook.
"I would like to state categorically that everything that has been approved and carried out at the private residence of the current president is in line with the Ministerial Handbook as far as it relates to security arrangements for private residences of the president," Nxesi told the paper.
"This is also the normal practice for the former presidents of South Africa."
Zuma's spokesperson Mac Maharaj told the Telegraph online that the president's Nkandla homestead needed to be upgraded to house his staff and those of visiting guests.
"What do you do when President [Barack] Obama or an African head of state visits him? You can't send them to a hotel," he was quoted as saying on Tuesday.
"Where do Prime Minister [David] Cameron's security staff stay when he goes to his private house? President Zuma's medical and security staff are inside that complex but you can't put them in the same house as his family."
The president should, on principle, not be expected to pay for security staff accommodation and guests out of his own pocket.
The Democratic Alliance called on Public Protector Thuli Madonsela to probe the allegations and for Zuma to cancel the upgrade.
"Reports that the department of public works will be spending millions on Zuma's private homestead is a serious abuse of taxpayers' money by a department which is failing in almost every other key responsibility," DA parliamentary leader Lindiwe Mazibuko said in a statement.
"This expenditure by public works represents a serious confusion by the president and the minister of public works as to what the pressing priorities for South Africa are," she added.
"[We] will not allow for this to go unanswered," said Mazibuko.
She said she wanted the Madonsela to investigate whether the money for the project had not been transferred from other projects that needed the funds.
The party also criticised the fact that the residence would be a private home and would not remain the state's property.
Political commentator Karima Brown said the unconfirmed reports were another example of how the media were targeting Zuma.
"Jacob Zuma has never been an easy fit for South Africa's chattering classes," she said.
"His existence challenges the notion of what it means to be black and middle-class in South Africa, and they will take any opportunity to attack him."
The City Press reported that the budget for the revamp was approved by the public works department in March last year.
According to the paper, Durban's public works regional manager Kenneth Khanyile wrote a memorandum last year to the then public works minister Gwen Mahlangu-Nkabinde saying their head office had assisted in apportioning costs between the department and Zuma.
Khanyile had reportedly informed Mahlangu-Nkabinde that they had already spent funds on certain building aspects which were initially meant to be catered for by Zuma.
"[Zuma] may want to implement these issues himself without the interference of the department or else he may want to opt to reimburse the department the same," Khanyile's memorandum was quoted as saying.
The presidency referred the City Press to the department of public works for answers but the department refused to give comment.
The "handling of information for this residence is protected in terms of the 1982 Protection of Information Act," the department's acting director general Mandisa Fatyela-Lindie was quoted as saying.
The revamped house would contain 10 air-conditioned rooms, underground living quarters, a clinic for Zuma and his family, 10 houses for security personnel, a helipad, houses for air force and police units, underground parking, playgrounds and visitors centres, said the City Press.
Worst audit option
Financial chaos continues to dog the public works department, according to Auditor General Terence Nombembe.
This resulted in Nombembe giving the department another disclaimer for the 2011/12 financial year – one of the worst audit opinions possible.
Nombembe said he could not rely on information provided by the department about, among other things, how many properties it owned and leased to sister departments and other state entities, and the accuracy of irregular, fruitless and wasteful expenditure.
"I was unable to obtain sufficient appropriate audit evidence to satisfy myself as to the completeness of irregular expenditure relating to the current year stated at R171,127,000 (2011: R1,396,000)."
The department's financial statements indicated there was over R69-million in fruitless and wasteful expenditure.
Nombembe said he could not rely on this figure either, as the department did not have a system in place to identify this type of spending.
The lease problems at the department continued.
"I was unable to obtain sufficient appropriate audit evidence for operating lease expenditure transactions with an estimated value of R48 513 867," said Nombembe.
Action against department officials accused of wrongdoing was lacking in various instances.
"Investigations have not been conducted into all allegations of financial misconduct committed by officials, as required by treasury regulations."
As a result of this failure, disciplinary steps were also not taken against officials suspected of such conduct.
On the supply chain management side, the department was faring poorly by contravening treasury regulations and procuring goods and services of a transaction value higher than R500 000.
Nombembe took aim at officials who played a part in awarding relatives, friends, partners or associates lucrative public works contracts
Some of these officials had not been sanctioned for fraud and corruption.
The department's leadership was criticised for not holding officials accountable for their actions.
"Instability in key leadership positions had a negative impact in providing effective leadership in the department."
There have been various changes and turnaround plans in the department in the past few years.
Public works has had three ministers at its helm in the past two years following Cabinet reshuffles by Zuma. – Sapa