The 95-year-old former democracy icon - battling for life with a recurring lung infection - completed two months of hospitalisation last week.
"Former President Nelson Mandela continues to receive treatment in hospital in Pretoria and doctors have indicated to President Jacob Zuma that the former president is making a slow but steady improvement," a statement from the presidency said late yesterday.
"The medical team also reiterated that although his health was improving steadily, Madiba still remained in a critical condition," it said, referring to Mandela by his clan name.
The statement was the first official update on Mandela's health condition since July 31.
The globally revered leader was admitted at Medi-Clinic Heart Hospital in Pretoria on June 8 with the infection. He turned 95 on July 18.
Last week, Mandela's ex-wife Winnie Madikizela had said he was now "breathing normally".
Doctors had managed to contain his lung infection but kept draining fluid from the lungs, Winnie told Sky News in an interview. "He is now breathing normally," she had said.
Mandela had a long history of lung problems, dating back to the time when he was a political prisoner on Robben Island during apartheid. While in jail he contracted tuberculosis.
Mandela, regarded the founding father of South Africa's multiracial democracy, served as the country's first black president from 1994 to 1999.
He left power after five years as president.
Mandela was awarded the Nobel Peace Prize in 1993.
He retired from public life in 2004 and has rarely been seen at official events since.
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