In the statement, Zuma said that doctors were doing "everything possible to get his condition to improve and are ensuring that Madiba is well-looked after and is comfortable." Madiba is Mandela's clan name.
The language used in the statement was the strongest yet concerning the health of Mandela, whose progress has been a matter of intense concern since he was rushed to hospital in the early hours of June 8.
On Saturday, the presidency, seeking to play down news reports about Mandela's deteriorating health, described his condition as "serious but stable."
Mandela, who was freed by the apartheid government in 1990 after 27 years of imprisonment, became South Africa's first black president after the country's first democratic elections in 1994. He retired from public life in 2004.
He has not been seen in public since the World Cup soccer final in South Africa in July 2010 and has been hospitalized four times since December, mostly for the pulmonary condition that has plagued him for years.
The South African government faced criticism over the weekend after it confirmed reports that the ambulance carrying Mandela to a hospital on June 8 had broken down, leaving him waiting on the roadside for 40 minutes until a replacement vehicle arrived.
Zuma said he had been assured by doctors that "all care" had been taken to ensure that Mandela's condition was not compromised during that time.
"There were seven doctors in the convoy who were in full control of the situation throughout the period. He had expert medical care," he said.
Media reports claiming that Mandela had suffered a cardiac arrest on that same night contained "no truth," he added.
Zuma appealed to South Africans and people across the world to pray for "Madiba, his family and the medical team that is attending to him during this difficult time."