President Jacob Zuma said Mr Mandela, 94, remained in a serious condition but that over the past two days his doctors had said the improvements in his health had been sustained.
Mr Zuma added that the former president “continues to engage with family”.
Speaking at a Youth Day celebration in South Africa, Mr Zuma asked the audience to join him in wishing Mr Mandela a happy Father’s Day.
As the leader of South Africa’s anti-apartheid movement, Mr 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 hospital stay is his fourth since December.