"I don't need a photo-op, and the last thing I want to do is to be in any way obtrusive at a time when the family is concerned about Nelson Mandela's condition," he told reporters aboard Air Force One ahead of his arrival in the country.
During his time in South Africa, Obama plans to visit Robben Island, where Mandela spent 18 of the 27 years he was in prison.
The former South African leader remains in hospital with a recurring lung infection. He is said to be in critical condition.
Mandela's ex-wife Winnie Madikizela-Mandela said he is showing "great improvement, but clinically he is still unwell."
She spoke with reporters Friday outside Mandela's former home in the Johannesburg township of Soweto.
"I'm not a doctor, but I can say that from what he was a few days ago there is great improvement," she said.
The South African government said Thursday that Mandela’s condition was stable. One of his daughters also said that he was able to open his eyes and respond to the touch of his family.
Madikizela-Mandela thanked supporters for their well-wishes, but also asked media to be more sensitive in their reporting of the former president's illness.
"We are just here to thank you very much for your support, and we had no idea of the love out there for us in our particular situation," she said. "And if sometimes we sound bitter, it is because we are dealing with a very difficult situation."
The news of Mandela's improvement seemed to lighten the mood outside the Pretoria hospital, where the 94-year-old was admitted earlier this month. Supporters have been standing vigil outside, sometimes singing and dancing in tribute to the anti-apartheid hero.
Dispute over burial
While South Africans waited for more news on the former president's health, members of Mandela's family are sparring over where he might be buried.
The South African Broadcasting Corp. reported Friday that a court ruled a grandson of Mandela must return the remains of three of the former leader's children to the family graveyard in the village of Qunu.
The grandson, Mandla Mandela, had previously exhumed the remains, which include those of his father, and taken them to the village of Mvezo, which is Nelson Mandela's birthplace. Mandla Mandela is the chief in Mvezo, and he reportedly wants to build a shrine to his grandfather, a hotel and a soccer stadium there.
Nelson Mandela's oldest daughter, Makaziwe, and 15 other family members asked the court to force Mandla Mandela to permit the exhumation of the bodies and their return about 20 kilometres to Qunu. Mandla Mandela has until Saturday to respond to the court order.
U.S. President Barack Obama arrived in South Africa on Friday as part of a three-country tour of the African continent. It remains uncertain whether he will have the opportunity to meet with Nelson Mandela, whom he calls a personal hero.
"I don't need a photo-op, and the last thing I want to do is to be in any way obtrusive at a time when the family is concerned about Nelson Mandela's condition," he told reporters aboard Air Force One.
During his time in South Africa, Obama plans to visit Robben Island, where Mandela spent 18 of the 27 years he was in prison.Suggest a correction