Mr Zuma said the doctors were doing everything they could to make the former leader comfortable, but he could not give any more medical details.
South Africa's first black president, 94, was taken to hospital in Pretoria earlier this month for the third time this year, with a lung infection.
A senior official said South Africans should not hold out "false hopes".
On Sunday, the presidency announced that Mr Mandela had become critical, after Mr Zuma visited him in hospital.
Mr Zuma said on Monday he had found Mr Mandela asleep, but had spoken to his wife and medical teams.
"All of us in the country should accept the fact that Madiba [Nelson Mandela's clan name] is now old. As he ages, his health will... trouble him and I think what we need to do as a country is to pray for him."
7 years ago