JOHANNESBURG (AFP) - South Africa, the country worst-hit by the coronavirus on the continent, has registered more than 10,000 daily cases as infections surge at an exponential rate, the health minister said.

The Covid-19 positivity rate - the proportion of tests that come back positive - has topped 21 per cent, far exceeding the "ideal" rate of 10 per cent, Health Minister Zweli Mkhize said in a tweet late on Wednesday (Dec 16).

South Africa reined in its first wave of the virus, which occurred in July, when the new cases topped 12,000 daily.

Numbers then gradually came down, to below 1,000 in September.

On Monday, the figure had risen to around 8,000, prompting President Cyril Ramaphosa to announce new restrictions, in particular a curfew from 11pm and the closure of some beaches in the south-east, at the start of the southern hemisphere summer.

"Today, we have breached the ten thousand mark for new cases," Mr Mkhize said. "Our daily cases are growing exponentially."

The worst-hit region is the Western Cape in the south, including the tourist destinations of Cape Town and the country's wine country, which had almost one-third of the 10,008 new cases.

Kwazulu-Natal in the south-east and the economic capital Johannesburg are the second- and third-worst hit.

"Our beaches are known for overcrowding during this time and people tend to be carefree," the minister said.

He urged holidaymakers who may be heading to those beaches that are open "to ensure that it does not become a day of regret where people get infected and lives are lost".

As of late Wednesday, the country of around 58 million people had recorded 23,827 deaths from 883,687 cases.

South Africa accounts for more than a third of the coronavirus cases reported across the African continent.