"They are simply being like puppies barking at the moon," Moloto Mothapo, spokesperson for the ANC chief whip told the Mail & Guardian.
"Bring us some concrete proof of alleged impropriety, then we will talk about taking action or following your lead. For the moment there is nothing and the president has done nothing wrong."
The Nkandlagate scandal came to light after a string of reports revealed that about R240-million would be forked out for infrastructural improvements at the president's private residence at Nxamalala in rural Nkandla, KwaZulu-Natal.
The project is chiefly financed by the public works department with the last payment reportedly taking place days before Zuma called for financial caution in light of current economic conditions – along with a pay freeze for senior public and private sector executives.
"The DA will continue to pursue steps to ensure that President Jacob Zuma and his government are held accountable," DA parliamentary leader Lindiwe Mazibuko told reporters in Cape Town.
Attempts to modify legislation
Chief to the DA's plans to have the matter investigated will be an attempt to modify legislation set out in the National Key Point Act of 1980, which Public Works Minister Thulas Nxesi has repeatedly used to defend and conceal the details of the upgrade.
"We reject any attempt to change national legislation, merely to score political points, with the contempt it deserves," Mothapo added.
"Unfortunately, the DA needs a majority to change any Act and the numbers are simply not on their side."
Along with this, the DA said Zuma acted "above the law" by violating the Executive Ethics Act which seeks to govern the conduct of members of Cabinet, deputy ministers and members of provincial executive councils.
The opposition party believes Zuma may have violated the Act by using his position to enrich himself and other people.
The DA has also called for more information on the location on all of South Africa's national key points as well as their expenses and running costs to be available for public scrutiny.
But, along with their initial calls for changes to the National Key Points Act, Mothapo dismissed the DA's plans.
"We will not accept any of those proposals – it's as simple as that. Their strategy is not to strengthen democracy but simply grab headlines," he said.
Mothapo added the DA's attempts to have the matter opened to debate in Parliament were likely to fail.
"It is my assumption that Parliament won't open itself up to these frivolous things," he said.
Acting speaker Nomaindia Mfeketo previously disallowed debate on Nkandla in the National Assembly at the previous sitting of the Parliament Oversight Authority.
In addition to the ANC lambasting plans to have Nkandlagate examined in Parliament, it has emerged that the Standing Committee on Public Accounts (Scopa) turned down an initial request for an investigation into the Nkandla matter.
"We have received the request, are looking at it and have taken a position that we won't start with an outright investigations from the beginning," Themba Godi, Scopa chairperson, told the M&G.
Godi said Scopa would engage the public works department and "see how they react".
"The renovations are being done by public works as per fulfilling their mandate – the same mandate they do for other departments."