The office of President Jacob Zuma thanked South Africans who prayed for 94-year-old Mandela at Easter church services this weekend, as well as people at home and around the world who showed their "love and support in various ways" for the anti-apartheid leader and his family.
"We also thank foreign governments for their messages of support," Zuma's office said in a statement.
The government "is satisfied that the doctors are providing the former president with the best medical care possible to enable his recovery and comfort. They have reported a further improvement in his condition," the statement said.
Mandela was admitted to a Pretoria hospital near midnight Wednesday. It was his third trip to a hospital since December, when he was treated for a lung infection and also had a procedure to remove gallstones. Earlier in March, he spent a night in a hospital for what officials said was a scheduled medical test.
"The whole world must come together and pray for him," Zacheus Phakathi, a security guard, said Sunday at an outdoor service on a hill overlooking Johannesburg.
In Pretoria, the capital, Henry Hyar, a restaurant waiter, standing by a hospital where Mandela is believed to be, said it was unfortunate that Mandela could not be with his family at home during Easter.
"I'm not happy about it," Hyar said. "We're praying for him to get better as soon as possible."
On Saturday, Zuma's office reported that Mandela was breathing without difficulty after having a procedure to clear fluid in his lung area.
Mandela became South Africa's first black president in 1994 after elections were held, bringing an end to the system of white racist rule known as apartheid. After his release from prison in 1990, Mandela was widely credited with averting even greater bloodshed by helping the country in the transition to democratic rule.
The Nobel Peace Prize laureate has been particularly vulnerable to respiratory problems since contracting tuberculosis during his 27-year imprisonment for fighting white racist rule in his country.
The elderly are especially vulnerable to pneumonia, which can be fatal. Its symptoms include fever, chills, a cough, chest pain and shortness of breath. Many germs cause pneumonia.
The office of President Jacob Zuma has said doctors were acting with extreme caution because of the Mandela's advanced age.
Associated Press television cameraman Bram Janssen contributed to this report from Pretoria.