The Democratic Alliance (DA) has written to President Jacob Zuma demanding that he release the terms of reference for a judicial commission of inquiry into State capture by Friday.

Zuma was given 30 days from December 13 in which to establish an inquiry, after the North Gauteng High Court rejected his bid to have former public protector Thuli Madonsela's recommendations on the inquiry set aside.

Zuma finally announced the establishment of the long-awaited commission last week, saying "the matter cannot wait any longer".

DA federal executive chairperson James Selfe on Thursday said that Zuma now needs to clarify the scope of the probe.

"The establishment of the judicial commission is so far beyond overdue it is astounding," he said in a statement.

"If the president had respected the Constitutional mandate of the Public Protector, the report on the findings of the judicial inquiry should have been finalised by June last year, a full seven months ago."

Those opposed to Zuma and State capture have called for narrow terms focusing on the influence of the Gupta family, among others, during Zuma's two terms.

Others, including Madonsela's successor Busisiwe Mkhwebane, have called for the scope to be widened, to include apartheid-era corruption.

Selfe though was critical of Mkhwebane's suggestion.

"Mkhwebane's proposal is neither practical nor in the interests of justice as it might result in the commission sitting for years and being unable to complete its work because of an overly broad mandate."

New ANC president Cyril Ramaphosa also believed the terms should conform to Madonsela's recommendations, he continued.

"It is time the ANC demonstrates their commitment to stamping out corruption, which has become rife under its watch. Failure to do so only confirms that the ANC under Ramaphosa will be the same as the ANC under Zuma."

Deputy Chief Justice Raymond Zondo will head the inquiry.

Zondo was recommended by Chief Justice Mogoeng Mogoeng, as recommended by Madonsela in her report.