Deputy Chief Justice Raymond Zondo will review allegations that the Gupta brothers – who headed one of the country’s largest conglomerates – unduly influenced Zuma over political appointments and winning government contracts.
The allegations and other scandals surrounding Zuma’s nine-year rule forced him out of office in February.
It was unclear on Monday whether he or the Guptas – who all deny any wrongdoing – will appear at the inquiry, which is empowered to make recommendations for prosecutions.
“The response has been quite disappointing. I would like to take this opportunity once again to ask the public to come forward with any information.
“If this commission is to do its job properly we need evidence,” he said.
Zondo said in May that the inquiry could last two years.
It stems from a 2016 report into alleged influence-peddling by the Public Protector, South Africa’s main anti-graft authority.
That report, which stopped short of asserting crimes had been committed, called for an investigation into whether Zuma, some of his cabinet members and some state companies acted improperly.
Among the cases it reviewed was an allegation by Deputy Finance Minister Mcebisi Jonas that the Guptas offered to secure him his boss’s job, as well as claims that Zuma directed state firms to award tenders to the Guptas.
Jacob Zuma says the three Gupta brothers – Atul, Ajay and Rajesh – are his friends but he denies any influence-peddling in their relationship.
The exact whereabouts of the Guptas are not known.
The brothers, officials from their companies and their family representatives could not be reached for comment on Monday.
South African judicial authorities have declared Ajay Gupta a “fugitive from justice”. He is known to have left South Africa for Dubai in February.
In a separate criminal case, Jacob Zuma is facing 16 charges of fraud, racketeering and money laundering relating to a deal to buy European military hardware to upgrade South Africa’s armed forces after the end of apartheid in 1994.
He denies the charges.
Cyril Ramaphosa, who succeeded him as president, has promised to crack down on graft and help revamp a stagnating economy that lost momentum and suffered credit downgrades during Jacob Zuma’s tenure.