Prince Harry and his wife Meghan Markle have met Archbishop Emeritus Desmond Tutu, a prominent anti-apartheid activist, with their four-month-old son Archie also making his first public appearance in South Africa.

The couple were spending their last day together in the South African city of Cape Town before the prince set off later on Wednesday to Botswana as part of their 10-day tour of southern Africa.

While he is away, the Duchess of Sussex will remain in South Africa with Archie.

The duchess held the four-month-old in her arms as she and Harry were greeted by Archbishop Tutu and his wife Leah.

The royals with Desmond Tutu. Photo: AAP

Until his meeting with the Archbishop, baby Archie had been seen in public only twice – a few days after his birth and at the polo with his parents. His christening was private, with two photos released afterwards.

The Tutus had called Wednesday’s meeting with the Duke and Duchess of Sussex a “rare privilege and honour” in a statement issued last week by the Desmond and Leah Tutu Legacy Foundation.

The meeting happened at the foundation, which is housed in a historic building in Cape Town built by slaves.

“The foundation is the global rallying point for the Archbishop’s values in respect of people and the earth,” said Niclas Kjellstrom-Matseke, its chairman. “We are enormously grateful to welcome the Duke and Duchess to our magnificent space.”

Later on Wednesday, Meghan met female entrepreneurs and investors working in technology.

Meghan Markle at another engagement later on Wednesday. Photo: AAP

In Botswana, Harry will on Thursday plant trees in the Chobe Forest Tree Reserve, visit an HIV project and dedicate an area of Chobe National Park to the Queen’s Commonwealth Canopy, a network of forest conservation initiatives.

After stops in Angola and Malawi, he will reunite with Meghan and Archie on October 1 in the South African city of Johannesburg, where they will wrap up their trip.

-with AAP