McKinsey has made sweeping changes to its South Africa business to try to rebuild its reputation following an ill-fated deal with friends of scandal-plagued former President Jacob Zuma.

Kevin Sneader, who started as McKinsey's global managing partner last week, announced on Monday that the firm has appointed a new head of its Africa division and replaced its South African finance, legal and compliance staff.

"On behalf of McKinsey & Company, I sincerely apologise to the people of South Africa. We are deeply sorry," Sneader told an often hostile audience of consultants, academics, NGOs and journalists at a Johannesburg business school.

"I hope you will allow us to earn back the trust we have lost," added Sneader, who was previously the head of McKinsey's Asian offices before his promotion.

Privately-owned McKinsey has lost many of its clients in South Africa since it emerged last year it had partnered with local consultancy Trillian in order to win a R1.6-billion ($120-million) contract with State power utility Eskom in 2016.

Trillian was then controlled by the Guptas, three brothers who are under investigation over accusations that they used their friendship with Zuma to fraudulently win government contracts worth hundreds of millions of dollars.

Zuma and the Guptas deny any wrongdoing. Police have a warrant of arrest out for at least one of the Gupta brothers.

South Africa's national prosecutor is considering pursuing a criminal case over the contract between McKinsey, Trillian and Eskom which it says was unlawful and a "sham".

McKinsey, the world's biggest consultancy, denies doing anything illegal.

McKinsey is among several multinational firms to have become ensnared in a far-reaching scandal that has outraged South Africans who have watched state resources being looted while millions remain mired in poverty.

"To be brutally honest – we were too distant to understand the growing anger in South Africa," Sneader said.

McKinsey said it will this week pay back the R1-billion ($74-million) in fees it received for its share of the six months' work it did with Trillian at Eskom.

The firm's critics say this doesn't go nearly far enough and urged the authorities not to let it off the hook.

"We will not be satisfied with anything other than criminal convictions," said David Lewis, director at Corruption Watch.

Some of the criticism McKinsey has faced is over the fee it charged for such a short period of work to a struggling state company that has fallen deeper into financial crisis since the consultancy's "turnaround programme".

McKinsey had previously defended its work at Eskom and its fees but Sneader said that position had changed.

"It is hard to be proud of our work on the turnaround programme given where Eskom is," Sneader told Reuters.

"The fee was too large."