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.
The former president and anti-apartheid leader has been critically ill with a recurring lung infection since 8 June.
South African President Jacob Zuma, who visited Mr Mandela in hospital, said he was "encouraged" by his progress.
South Africans have been urged to mark Mr Mandela's 67 years of public service with 67 minutes of charitable acts.
"When I visited him today... I was able to say 'happy birthday' and he was able to smile," Mr Zuma said in a statement.
"Mandela's struggle for freedom and justice in our country and his values of promoting a fair, just and equitable world continues to inspire and motivate us," he told a visiting EU delegation.
Mr Mandela's daughter, Zindzi, said he was making "remarkable progress", and that she had found him watching television with headphones on and communicating with his eyes and hands when she visited him this week.
"We look forward to having him back at home soon," the South African Press Association quoted her as saying.
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 multi-racial elections in 1994.
The governing 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.
Activities throughout the day included:
- School-children across the country singing a synchronised Happy Birthday to the former president
- Mandela family members handing out gifts to Mamelodi township residents before holding a birthday lunch with Nelson Mandela. They have prepared 95 cupcakes in his honour
- President Zuma visiting Mr Mandela in hospital and overseeing the donation of houses to poor white families in the Pretoria area
- Volunteers spending 67 minutes each renovating schools and orphanages, cleaning hospitals and distributing food to the poor to mark the former statesman's 67 years as a lawyer, activist, prisoner and president
- Mr Mandela becoming the first recipient of South Africa's new Smart ID Card, introduced on Thursday. His card will be collected on his behalf by his daughter Zindzi
- The forming of a human chain from Johannesburg's Fashion District into the heart of the city
Events are also 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, speaking in a recorded message, has pledged 67 minutes of community service on Thursday to "make the world a better place, one small step at a time".
Meanwhile, concerts are planned later this week in the Australian city of Melbourne, featuring local and African artists.
Mr Mandela's ill-health gives extra poignancy to this year's Mandela Day, correspondents say.
For South Africans, the best birthday present for Mandela would be for him to recover and be among the people who love him most, says the BBC's Pumza Fihlani in Johannesburg.
Winnie Madikizela-Mandela told a local radio station her former husband's 95th birthday was "a gift not only to the family... but to the nation".
She rejected the "prophets of doom" who have warned of chaos in South Africa when Nelson Mandela dies.
"The country will solidify and come together," she told Radio 702.
Mr Mandela's 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.