Orania has a vacancy for a new leader after its president, Carel Boshoff, stepped down at a leadership meeting on Friday.
Orania is a whites-only town situated on the banks of the Orange River in the Northern Cape.
In a statement, Orania Movement spokesperson and deputy president Sarel Roets said that Boshoff had announced his resignation at the meeting "to accept responsibility for governance flaws during his tenure, though these are not attributed to him personally".
Roets added that Boshoff had said he wanted to take on new challenges and make way for new leaders.
This follows reports of irregularities at the organisation.
The purchase of a Mercedes-Benz, a 45% salary increase, and a long list of accusations of mismanagement and infighting are some of the issues that had plagued Boshoff, as well as his organisation, Netwerk24 reported in April.
Boshoff is a grandson of Hendrik Verwoerd, a former apartheid prime minister.
Roets said that there was never any discussion about any offences by any of its officials.
Roets said a motion was adopted that the structure of the Orania Movement - and specifically the duties of its president, executive committee and CEO - should be redefined.
"This emanates from the enormous growth the organisation has seen in the past few years, and the great pressure it has placed on exiting staff and infrastructure," he said.
An acting operations manager would be appointed in the meantime to implement recommendations on procedures and governance by a task team.
Roets said, "in healthy democracies, leaders stand down to accept responsibility for political voids, even when there was no wrongdoing or corruption", citing the resignation of UK prime minister Theresa May as an example.
According to reports by Beeld and Volksblad, complaints against Boshoff included that he unlawfully purchased and used a Mercedes-Benz for R102 000, and that he increased his salary, called the "president's honorarium", by 45% to R22 000 per month.
This was done reportedly because he had been expected to perform additional office duties.