"Madiba is fine, Madiba is getting better and better," the private eNCA news channel quoted Graca Machel as saying, referring to Mandela's clan name.
"He is in hospital simply because the doctors want to be absolutely sure that he is strong enough to go home and nothing is going to recur," she said.
President Jacob Zuma, who visited the revered statesman on Thursday, said Mandela is making "continuous improvement" in the hospital.
"President Jacob Zuma visited former President Nelson Mandela in hospital today, 4 April 2013, and received a briefing from doctors which indicate continuous improvement in his condition," Zuma's office said in a statement.
"Madiba is stable and we are thankful that he is responding well to treatment and that he is much better. We remain thankful for all the support to the family during this difficult time," the president said.
The 94-year-old Nobel Peace Prize laureate, often fondly called by his clan name 'Madiba', was re-admitted to an undisclosed hospital in Pretoria shortly before midnight on March 27, his third stay since December.
Earlier in March, Mandela spent a night at a Pretoria hospital where he underwent a successful medical examination.
In December, he was admitted for 18 days for treatment of the lung infection and surgery to extract gallstones. It was his longest stint in hospital since his release from prison in 1990.
Mandela had a long history of lung problems, dating back to the time when he was a political prisoner on RobbenIsland during apartheid. While in jail he contracted tuberculosis.
Mandela served as South Africa's first black president from 1994 to 1999 and is widely regarded as the father of the nation for leading the struggle against apartheid and for democracy.
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