South Africa will be rolling out a plan that aims to have 31,000 vaccinations done a day, as the country with 58.6 million people battles the highest number of coronavirus infections in the African continent.

Citing the latest statistics, the nation's Health Minister Zweli Mkhize said on Sunday the number of cases had risen to 1.4 million, up 8,147 from the day before.

In the same period, 300 more people died from Covid-19-related causes, bringing the total to 40,874 since the start of the pandemic, according to a government statement on Sunday.

South Africa, which was the first country in Africa to record more than one million cases at the end of last year, has a recovery rate of 87 per cent, it added.

But unlike some other badly hit countries, South Africa has yet to start its vaccination programme, although it is the richest nation in Africa, the BBC said last week.

Opposition leaders alleged that the government started talks with vaccine suppliers only early this month. Concerns have also risen that infections are driven in part by a new strain called 501.V2, which may be more infectious, the BBC reported on Monday. It remains unknown how this variant will respond to existing vaccines.

South Africa's vaccination programme will not be available for everyone immediately, Cape Argus newspaper reported on Sunday. It said a priority system will be in place for the plan that aims to inoculate 67 per cent of the population or about 40 million people.

The first phase will target 1.25 million people, primarily front-line healthcare workers, while the second phase will cover another 16.6 million people, including police officers, miners, staff in banking and those above 60 years old.

The third phase aims to inoculate another 22.5 million people aged above 18.

The government has not provided a detailed timeline on the vaccine roll-out, Cape Argus said, though the country has reportedly secured around 34.5 million doses of vaccines.

The report added that about one million doses are expected to reach the country by the end of this month from the Serum Institute of India, which is producing the vaccine developed by AstraZeneca and the University of Oxford.

Another 500,000 doses are expected to arrive next month.

The order from AstraZeneca and the University of Oxford comprises about 70 per cent of the total vaccines South Africa will be getting, Dr Mkhize told Parliament earlier this month.

Vaccines from Johnson & Johnson will account for 20 per cent of the supply while those from Moderna and Pfizer-BioNTech will make up 5 per cent each, he added.

A Department of Health spokesman said negotiations with suppliers are ongoing.

"We're aiming at securing vaccines from multiple countries so as to minimise the risk of short supply," he said.

South Africa is part of the World Health Organisation's global scheme for a fair distribution of vaccines against Covid-19, called Covax.

It is expected to acquire doses for around 10 per cent of the population through Covax from April to June, the BBC said last week.