He said there had been a global outpouring of messages expressing concern for Mandela's health.
Zuma wished Mandela a speedy recovery, referring to him affectionately by his clan name, "Madiba."
"We appeal to the people of South Africa and the world to pray for our beloved Madiba and his family and to keep them in their thoughts. We have full confidence in the medical team and know that they will do everything possible to ensure recovery," the presidential statement quoted Zuma as saying.
Mandela spent a night in a hospital and was released on March 10 following a medical test. At that time, spokesman Maharaj said Mandela was "well."
In February 2012, Mandela spent a night in a hospital for minor diagnostic surgery to determine the cause of an abdominal complaint. In January 2011, he was admitted to a Johannesburg hospital for what officials initially described as tests but what turned out to be an acute respiratory infection. He was discharged days later.
He also had surgery for an enlarged prostate gland in 1985.
Under South Africa's white-minority apartheid regime, Mandela served 27 years in prison, where he contracted tuberculosis, before being released in 1990. He later became the nation's first democratically elected president in 1994 under the banner of the African National Congress, helping to negotiate a relatively peaceful end to apartheid despite fears of much greater bloodshed. He served one five-year term as president before retiring.
Perceived successes during Mandela's tenure include the introduction of a constitution with robust protections for individual rights and the Truth and Reconciliation Commission, a panel that heard testimony about apartheid-era violations of human rights as a kind of national therapy session. South Africa still struggles with crime, economic inequality and other social ills.
Mandela last made a public appearance on a major stage when South Africa hosted the 2010 World Cup soccer tournament.