President Jacob Zuma said Mandela remains in serious condition but that over the last two days his doctors have said that the improvements in his health have been sustained.
Zuma said Mandela "continues to engage with family," according to the prepared text of a speech released by the president's office. Family members are visiting Mandela daily.
The leader of South Africa's anti-apartheid movement, Mandela spent 27 years in prison during white racist rule. He was freed in 1990 and became South Africa's first black president in 1994. His hospitalization in Pretoria, the capital, is Mandela's fourth admittance for treatment since December.
Zuma asked the audience at a Youth Day celebration to join him in wishing Mandela a happy Father's Day.
Youth Day commemorates June 16, 1976, when school children from the township of Soweto marched in protest of a government order that half of all classes in secondary school must be taught in Afrikaans, a derivative of Dutch spoken by the descendants of European settlers.
Police fired on the young marchers with live ammunition. Hector Pieterson, a 13-year-old boy, was the first one killed. In all, hundreds of children - who fought the police with sticks and rocks - were wounded or killed in the violence.
Zuma said the youth of 1976 "took on the might of the apartheid state" and that Pieterson "became a symbol of the student uprising and quest for freedom and a better life."
"The bravery of our youth during those difficult times pushed our country closer to freedom and democracy which we finally achieved in 1994," Zuma said.
Leeann Foster visited the Pieterson memorial on Sunday, where many people had Mandela on their minds.
"It's a bit strange that he's not here to celebrate with us as he has done so much for the struggle. But I think that we should all be grateful and appreciate what he's done so far for us and pray for a speedy recovery," Foster said.
Mandela, Nobel Peace Prize winner, has been particularly vulnerable to respiratory problems since contracting tuberculosis during his long imprisonment. The bulk of that period was spent on Robben Island, an outpost off the coast of Cape Town where Mandela and other prisoners spent part of the time toiling in a stone quarry.
Associated Press Television News reporter Bram Janssen contributed to this report.