Obama did not visit Mandela, 94, who has been hospitalized in Pretoria for three weeks with a severe lung infection.
He talked with Mandela's wife, Graca Machel, on the telephone and met with other members of the family at the Mandela Foundation in Johannesburg.
"I expressed my hope that Madiba draws peace and comfort from the time that he is spending with loved ones, and also expressed my heartfelt support for the entire family as they work through this difficult time," Obama said, using Mandela's clan name. "I also reaffirmed the profound impact that his legacy has had in building a free South Africa, and in inspiring people around the world -- including me."
Mandela, who spent years in prison on Robben Island under South Africa's apartheid government, went on to become its first black president. Obama plans to visit Robben Island Sunday.
Obama announced Saturday he is launching a program to bring young leaders from South Africa and other African countries to the United States as Washington Fellows. He told an audience of more than 600 young people from South Africa, Uganda, Kenya and Nigeria that the program will begin in 2014 and offer 500 fellowships annually.
The fellows will spend time at top U.S. universities and have an opportunity for internships with businesses and government agencies. The goal is to foster a generation of leaders in public affairs and private enterprise.
The meeting between Obama and Zuma also included talk of Mandela.
"The triumph of Mandela speaks to something deep in human spirit; a yearning for justice and dignity which transcends ... bounds of race," Obama said at a news conference after the meeting.
Zuma linked Mandela and Obama "as the first black presidents of your respective countries, thus you both carry the dreams of millions of people in Africa and in the Diaspora who were previously oppressed," The New York Times reported.
Obama and his family arrived in South Africa Friday from Senegal. He talked with Senegalese farmers and business owners about technologies to improve farming conditions in the region.
The Obamas were to wrap up the African trip with a two-day stop beginning Monday in Tanzania.