Several hundred people gathered at the Regina Mundi church in Soweto – once a focal point of the struggle against apartheid.
On Saturday, South Africa’s presidency said Nelson Mandela, 94, was breathing without difficulty.
It said excess fluid had been drained from the lungs to ease his breathing.
There are no details yet on how long he will remain in hospital and no statement on his condition has been given for the past 24 hours.
After Nelson Mandela was admitted to hospital late on Wednesday, South Africa’s President Jacob Zuma said people “must not panic”.
Nelson Mandela contracted tuberculosis in the 1980s while detained on windswept Robben Island.
His lungs are said to have been damaged while working in a prison quarry. This latest spell in hospital is his fourth in just over two years.
Nelson Mandela served as South Africa’s first black president from 1994 to 1999 and is regarded by many as the father of the nation for leading the struggle against apartheid.
The statement read by presidential spokesman, Mac Maharaj, on Saturday said that Nelson Mandela had been admitted to hospital “due to a recurrence of pneumonia”.
It said: “Doctors advised that due to the lung infection, former President Mandela had developed a pleural effusion which was tapped. This has resulted in him now being able to breathe without difficulty.
“He continues to respond to treatment and is comfortable.”
Mac Maharaj, a prisoner on Robben Island with Nelson Mandela in the 1960s and 70s, said the presidency “would like to acknowledge and thank all who have been praying for, and sending messages of support for, Madiba and his family.”
Madiba is Mandela’s clan name and is widely used to refer to him.
The hospital Nelson Mandela is attending has not been disclosed.
Last December Nelson Mandela was treated for a lung infection and gallstones – his longest period in hospital since leaving prison in 1990.
In February, the former president was treated for a stomach condition.
When asked whether people should prepare for the inevitable, President Jacob Zuma said: “In Zulu, when someone passes away who is very old, people say he or she has gone home. I think those are some of the things we should be thinking about.”
But the president stressed that Nelson Mandela had been able to handle the situation “very well” so far.
South Africans have been praying for the recovery of Nelson Mandela, who remains a moral beacon in the country despite withdrawing from public life almost a decade ago.
Despite his long imprisonment, Nelson Mandela forgave his former enemies and as president urged South Africans of all races to work together and seek reconciliation.
In 1993 Nelson Mandela was awarded the Nobel Peace Prize.
His main home is in Qunu, a small rural village in Eastern Cape province, where he says he spent the happiest days of his childhood.
However, doctors said in December Nelson Mandela should remain at his home in the Johannesburg neighborhood of Houghton to be close to medical facilities.
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