The revered ex-leader remained in a serious condition as he recovered from a lung infection, BBC reported Zuma as saying.
"Over the last two days, although he remains serious, his doctors have stated that his improvement has been sustained," Zuma said, adding that the 94-year-old anti-apartheid icon "continues to engage with family".
Zuma made the remarks while addressing a gathering for Youth Day in KwaZulu-Natal province in remembrance of the 1976 Soweto uprisings against apartheid.
The president asked the audience to join him in wishing Mandela a happy Father's Day.
Mandela has been in and out of hospital several times since last December.