"Madiba is stable and we are thankful that he is responding well to treatment and that he is much better," Zuma said in a statement.
Mandela, also known by his clan name "Madiba", was admitted shortly before midnight on Wednesday, March 27, with pneumonia.
"We remain thankful for all the support to the family during this difficult time."
Zuma also met members of the family, who expressed their gratitude for the support from South Africans and people all over the world, his spokesman Mac Maharaj said.
Mandela, now 94, has fought off at least three respiratory infections since January 2011. In the late 80s he was diagnosed with tuberculosis while in Pollsmoor Prison, and successfully treated.