Police Minister Fikile Mbalula has postponed the briefing intended to outline the processes involved in the appointment of a new head for the Directorate for Priority Crime Investigation.
A briefing was scheduled to take place at the Johannesburg Central police station, but it was postponed in a brief statement.
"The planned Media Briefing has been postponed and a future date will be communicated in due course," read a statement from the ministry.
The position was left vacant after Major-General Berning Ntlemeza was forced out in April following a ruling by the North Gauteng High Court in Pretoria that his appointment was irregular and unlawful.
He has since retired.
Lieutenant-General Yolisa Matakata was appointed the acting Hawks head.