A helicopter has been used in the hunt for the three-year lion that is thought to have slipped through a hole in the fence at Karoo National Park in the south of the country on Friday night.
"Aerial and foot patrols over the weekend have not yet yielded the desired results," South African National Parks said in a statement yesterday.
"Although the trackers picked up the lion's spoor on a number of occasions, the terrain is mountainous, with many river valleys, thus making tracking difficult."
"Members of the public who may see the lion or any signs of it are requested not to confront it," the statement added.
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Last week, a 29-year-old female US tourist was mauled to death by a lion in a Johannesburg game park after she wound down the windows of car she was travelling in and was attacked.
The lion from the Karoo National Park is believed to have been forced out by older males.
"The lion then... Entered private property through a storm water drain.
"Tracker teams, including tracking dogs and their handlers, have been sent... To assist in the search. The aerial and foot patrols are still ongoing.