Nelson Mandela is spending his 95th birthday in hospital in Pretoria, as events take place around the world and in South Africa in his honour.
South Africans are being urged to match the former president and anti-apartheid leader’s 67 years of public service with 67 minutes of charitable acts.
Mr Mandela, who is in critical but stable condition with a recurring lung infection, entered hospital on 8 June.
“We are proud to call this international icon our own as South Africans and wish him good health,” Mr Zuma said in a statement.
“We thank all our people for supporting Madiba throughout the hospitalisation with undying love and compassion,” he said, referring to Mandela’s clan name.
Mr Mandela’s daughter, Zindzi, said on Wednesday that he had made “dramatic progress”.
“I should think he will be going home anytime soon,” she told UK Sky TV.
Mr Mandela’s birthday is also Nelson Mandela International Day, a day declared by the UN as a way to recognise the Nobel Prize winner’s contribution to reconciliation.
The former statesman is revered across the world for his role in ending apartheid in South Africa. He went on to become the first black president in the country’s first all-race elections in 1994.
The ruling African National Congress (ANC) said that on this Mandela Day homage was being paid to 95 years of “life well-lived”, dedicated to the liberation of South Africans and people all over the world.
The day kicks off with millions of school children across South Africa singing Happy Birthday to Mr Mandela.
To mark the former statesman’s 67 years as a lawyer, activist, prisoner and president, volunteers will spend 67 minutes renovating schools and orphanages, cleaning hospitals and distributing food to the poor.
President Zuma plans to mark the occasion by overseeing the donation of houses to poor white families in the Pretoria area.
A poster project offering a global vision of Mandela, with 700 submissions from around the world, will be unveiled on Wednesday and auctioned off for charity.
“He carries across this concept of humanity and selflessness,” said Mohammed Jogie, co-founder of the project.
Events will also be taking place internationally, with an image of a large Mandela painting by South African artist Paul Blomkamp featured in New York’s Times Square.
British entrepreneur Richard Branson has pledged 67 minutes of community service on Thursday to “make the world a better place, one small step at a time”, speaking in a recorded message.
Meanwhile, concerts are planned later this week in the Australian city of Melbourne, featuring local and African artists.
His illness gives extra poignancy to this year’s Mandela Day, correspondents say.
For South Africans, the best birthday present for Mandela would be to recover and be among the people who love him most, says the BBC’s Pumza Fihlani.
As the family and millions around the country reflect the role Mr Mandela played in South Africa, there will be a quiet prayer that he will return home soon, our correspondent adds.
His third wife, Graca Machel, said last Friday that she was “less anxious” about his health than before and that he was continuing to respond well to treatment.
Thursday also is the 15th anniversary of the couple’s marriage.
Ahead of the anniversary, Mr Mandela’s close friend and lawyer George Bizos described them as “a loving couple”, the AFP news agency reports.
Meanwhile, Mr Mandela’s granddaughter Ndileka told the BBC on Wednesday that she had been hurt by a continuing family feud over the burial place of three of Mr Mandela’s children, as well as his own resting place.
She also described how difficult it had been for the family to cope with his critical illness, complaining of intrusive media questioning.