Nelson Mandela is said to be "breathing without difficulty" after responding well to treatment following his diagnosis with pneumonia.
Messages of concern poured in from around the world as the former South African president spent a third day in hospital, following his admission on Wednesday.
Mandela underwent a painful operation in which a tube was inserted into his lung to drain a build-up of fluid known as a pleural effusion, or "water on the lungs".
A statement from the office of the South African President, Jacob Zuma, said: "He continues to respond to treatment and is comfortable. This has resulted in him now being able to breathe without difficulty."
Mandela's grandson, Mandla Mandela, an MP with the African National Congress, said: "We have been blessed as a family to have my grandfather all these years with us. We have cherished every moment and continue to do so."
There were no immediate plans for his return home, said Mandla Mandela, though he was in good spirits and making steady progress.
"He sat up and had his breakfast in bed," Zuma's spokesman Mac Maharaj, who was jailed with Mandela during the apartheid era, told Agence-France Presse.
There were no immediate details on how long Mandela would remain in hospital.
It is the second time this month that Mandela has been admitted since being kept in for checks on 9 March following a three-week hospital stay in December, when he was treated for a lung infection and underwent surgery to remove a gallstone.
Mandela contracted tuberculosis in 1988 during his 27-year imprisonment on Robben Island under the apartheid regime. He has also undergone treatment for prostate cancer and numerous stomach ailments.
"It is good news but we need to be cautious, bearing in mind his age," said Maharaj.
Mandela has not made a public appearance since the World Cup football final in South Africa in 2010.
The name and location of the hospital where he is being treated have not been disclosed. In the past he has been treated at a clinic in Pretoria.