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"The SIU, and its head, are deeply conscious of the intense public interest in its report," spokesman Boy Ndala said in a statement.
"We also acknowledge that we are accountable to the public for the work we do."
However, the SIU Act did not empower the unit to release the report or make its contents public, he said.
The SIU handed its final report on the R246 million upgrades to Zuma's private Nkandla homestead in KwaZulu-Natal to him on Thursday, a week after the president submitted a response to National Assembly Speaker Baleka Mbete.
The presidency said he had taken all reports into account.
There were three different investigations into the upgrades, done by the joint standing committee on intelligence, the public protector, and the SIU.
Earlier this year, Public Protector Thuli Madonsela found Zuma and his family had unduly benefited from the upgrades and recommended that he repay some of the money.
Zuma declined to respond to Madonsela's report in full within the required fortnight and said instead he would wait for the SIU's findings.
Public spending on the security upgrades have turned into one of the major controversies of the Zuma presidency, as costs escalated to R246 million. It emerged the project included a pool (dubbed a "firepool" by government), an amphitheatre, a cattle kraal, and a chicken run, among others.
Last Friday, Madonsela's office said the response handed to Mbete by Zuma did not respond to Madonsela's report.
The presidency and the African National Congress's Chief Whip Stone Sizani disagreed with Madonsela's statement, saying Zuma had responded.
The National Assembly on Tuesday resolved to set up an ad hoc committee to consider Zuma's response.
Parliament's question time was suspended, then adjourned on Thursday when the Economic Freedom Fighters started shouting "pay back the money" to Zuma and indicated it was not happy with his answer as to when he would pay back some of the money spent on Nkandla, as recommended by Madonsela.