Jacob Zuma said he had visited Nelson Mandela and spoken to his wife and medical teams.
Doctors were “doing everything possible to get his condition to improve” said Jacob Zuma in a statement.
Nelson Mandela, 94, was taken to hospital in Pretoria earlier this month for the third time this year, with a lung infection.
Jacob Zuma said he had been told by doctors that the former president’s condition had worsened over the past 24 hours.
“The doctors are doing everything possible to get his condition to improve and are ensuring that Madiba is well-looked after and is comfortable. He is in good hands,” said Jacob Zuma, using Nelson Mandela’s clan name by which he is widely known in South Africa.
Jacob Zuma appealed for prayers for Nelson Mandela and his medical team.
Mac Maharaj, Jacob Zuma’s spokesman, said the doctors’ use of the word “critical” was “sufficient explanation that should raise concern amongst us”.
“Therefore we want to assure the public that the doctors are working away to try and get his condition to improve,” he said.
The release of information relating to Nelson Mandela is always carefully controlled by the government to avoid sparking alarm.
The use of the word “critical” to describe his condition will be seen as very worrying by South Africans, many of whom see him as like a family member.
There has been little information about Nelson Mandela’s condition in recent days. On June 13 Jacob Zuma, who releases all official updates relating to the much-loved leader, said his health continued to improve but that his condition remained serious.
More recently, one of Nelson Mandela’s grandsons, Ndaba Mandela, said his grandfather was getting better and he hoped he would be home soon.
Nelson Mandela’s wife, Graca Machel, thanked all those who had sent messages of support, saying they had brought “love, comfort and hope”.
The former president is revered for leading the fight against white minority rule in South Africa and then preaching reconciliation despite being imprisoned for 27 years. He left power after five years as president.
He is believed to have suffered damage to his lungs while working in a prison quarry.
He contracted tuberculosis in the 1980s while being held in jail on the windswept Robben Island.
Nelson Mandela retired from public life in 2004 and has rarely been seen at official events since.
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