Today's statement was the first time that officials said Nelson Mandela is suffering from pneumonia.
South African presidential spokesman Mac Maharaj said the former president had fluid on the lung caused by pneumonia, by he was now breathing more easily because the liquid had been "tapped".
Previous statements said he had been suffering from a lung infection.
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Thousands of people have linked hands on Westminster Bridge in a show of solidarity - one week after the terror attack in the capital.
PC Keith Palmer, 48, stabbed by Khalid Masood while on duty in the grounds of the Palace of Westminster last Wednesday.
Engineering firm CH2M won the £170 million contract but have pulled out of phase two of the project over alleged conflicts of interest.