The 94-year-old was taken to hospital in Pretoria on June 4 for the third time this year, with a lung infection.
His condition became critical on Sunday.
"Doctors continue to do their best to ensure his recovery, well-being and comfort," the latest update said.
President Zuma thanked the South African public for "ongoing support and understanding".
"We must support him and support his family. We must demonstrate our love and appreciation for his leadership during the struggle for liberation and in our first few years of freedom and democracy by living out his legacy and promoting unity, non-racialism, non-sexism and prosperity in our country," the President said.
Mr Mandela will turn 95 on July 18.
"We must all be planning what to do next month in marking our 67 minutes of doing good for humanity as called upon by Madiba to do so, when he launched the International Mandela Day campaign.
"Let us make it the biggest Mandela Day ever on the 18thof July, focusing on doing good all over the country,'' Zuma added.
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