Jacob Zuma, the outgoing South African President, established a long-awaited commission of inquiry on Tuesday to investigate allegations of private interests having steered his government's policy.
Zuma said Deputy Chief Justice Raymond Zondo - who was selected by Mogoeng - would lead the commission.
The rally has since stalled, with signs of higher rates in the United States shifting some of the focus back to fundamentals, although analysts said a decision on Zuma remained the main swing factor.
He says he was concerned that a further delay in the matter would make the public doubt government's commitment to fighting corruption.
"Regarding the terms of reference for the inquiry, the prima facie evidence and remedial actions, as stated by the former Public Protector, should form the basis thereof".
"I am also mindful of the concerns raised by the public protector in her report, wherein she lamented the lack of resources to conduct a wider inquiry into this matter", said Zuma.
"I have decided that‚ while the issues determined by the order require final determination by higher courts‚ this matter (state capture) can not wait any longer".
Mkhwebane said that after she had "perused" some of the information available, she called upon Zuma to ensure the terms of reference were "broad enough to include the capture of all state institutions and SOEs, so that the ability of the Commission to uncover the full extent of State Capture in South Africa is not constrained in any manner".
"Accordingly, by making more resources available, it is my honest hope that the commission will be able to reach many of those areas of concern that may not have been reached by the public protector's investigation, but form part of what she might have investigated, had she had sufficient resources to do so".
The Guptas allegedly exert undue influence on Zuma in the appointment of cabinet ministers and in the awarding of lucrative contracts with state-owned enterprises to the Guptas in what is called "state capture".
Madonsela released a report‚ titled State of Capture‚ in November a year ago concerning allegations of an improper relationship between Zuma‚ other state officials and the Gupta family.
Zuma's about-turn came a day before the new top leadership of the ANC met for the first time on Wednesday in the southern city of East London.
The ANC's elective conference in Johannesburg last month ruled the inquiry should be expedited.