The state government of Limpopo said the pride had been seen near the town of Phalaborwa, close to the borders with Zimbabwe and Mozambique.
It told members of the public to be “alert at all times” until the animals were recaptured.
“We want to assure the public that they need not panic as the situation is under control,” Zaid Kalla, a provincial government spokesperson, told local media.
It was not clear how the lions had escaped from the park, which is surrounded by fences designed to protect animals and local communities.
Local authorities said the lions would be returned to the park after recapture despite criticism from a spokesman for the Kruger who said the plan was not feasible.
The lions will continue to break out because other dominant lions will chase them out,” Ike Phaahla told South African state television.
“We need to identify a park where they can be taken and establish their own area … There is the possibility of wildlife-human conflict, so people have to be careful,” he said.
It was not clear how long the lions had been at large. Experts say the fence around the park is in good condition but that it can never stop all movements by animals.
The Kruger park covers nearly 2m hectares and is home to more than 500 bird and 147 mammal species. An estimated 2,000 lions live in the park.
A suspected rhino poacher was trampled by elephants then eaten by a pride of lions in the Kruger in April. Earlier this week, a leopard killed a two-year-old boy inside a fenced-off staff compound.
A team of rangers shot dead two leopards to avoid the risk of further attacks.
This article was first published by The Guardian on 7 June 2019.