Zuma's son Duduzane, who held a directorship in the company after starting there as an intern a few years ago, has also resigned amid a political storm over the issue.
The three Gupta brothers - Ajay, Atul and Rajesh - have been under immense pressure for the past few months after several high-ranking members of the ruling African National Congress (ANC), including the current Deputy Minister of Finance, claimed that the family had offered them government positions, including appointments as ministers.
There have been widespread calls from several compatriots and aides of late President and anti-apartheid icon Nelson Mandela as well as civil society and churches for Zuma to resign in the wake of the allegations and a finding by the country's highest judicial body, the Constitutional Court, that he had breached his duties in terms of the Constitution.
But the ANC has come out in defence of their leader.
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Simultaneous pressure on the Guptas has seen Oakbay's banks and financiers all severing their association with the business in the past fortnight.
Oakbay's executive committee and the CEOs of each of the businesses will continue to oversee the management and running of the business and all portfolio companies going forward.
The Guptas cited the risk to its thousands of employees and their dependents as having influenced their decision.
"By stepping down from all executive and non-executive positions and any involvement in the business, we hope to save the livelihoods of tens of thousands of people in our great rainbow nation," it said.
Reacting to allegations that the company had benefited unfairly from government contracts, Oakbay said less than 1 per cent of its revenue was from government contracts.