The unease among investors this week was partly stoked by the collapse of Steinhoff, whose investors rushed to sell stock.
Ron Klipin, a portfolio manager at Cratos Wealth, said the market was concerned that EOH senior management were not buying shares. But Zungu said he planned to take up further stock "with my own money".
Klipin said the deals Keating did with Sita and the police had dented credibility.
"It's the latest thing that has emerged that appears to have got the market rattled," he said, adding that market was more risk averse following the Steinhoff debacle.
The JSE had been in touch with EOH, according to John Burke, director of issuer regulation at the bourse.
Burke said EOH "confirmed to the JSE they were not aware of any price-sensitive information which would require an announcement".
Based on the unusual volatility in the share price, the company had issued a voluntary announcement, he said. The JSE would act on any reports or identification of potential market abuse.
Zungu said the audit committee "will inform the board what next to do". The audit committee would review the impact of reversing the purchases.
"We want to go back to the investor community and public at large with detail," he said.
EOH was unlikely to collapse, he said.
"The underlying business is fundamentally very strong. We have strong businesses. We do not have debt facilities that can be pulled by a bank. We have no bonds that will mature. We are basically ungeared," said Zungu.
The company was talking to shareholders. "I don't think people must sell in fright because they will be disadvantaging themselves. We need to quantify issues, losses and that's what we'll do next week."
Sita said it had handed over the relevant information to Ipid.
"We are committed to collaborate, support and work with all government institutions, to ensure that the rule of law applies equally to all," it said. It is not conducting an internal investigation
.