In a statement, the Presidency said doctors were "still doing everything they can" to ensure 94-year-old Mandela's well-being.
Zuma had been due to visit to Maputo today (Thursday), where he was to attend the SADC Regional Summit on Infrastructure Investment.
Mr Mandela, known by his clan name Madiba, 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.
Mr Zuma reiterated his "gratitude on behalf of government, to all South Africans who continue to support the Madiba family".
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