Thousands of South Africans have joined dozens of world leaders for the national memorial service for Nelson Mandela.
The service is being held in front of a vociferous crowd in the FNB stadium in Johannesburg.
President Barack Obama said Nelson Mandela was a “giant of history”, adding: “The world thanks you for sharing Nelson Mandela with us.”
Nelson Mandela, South Africa’s first black president died last Thursday, aged 95.
South Africa is observing a series of commemorations leading up to the funeral on Sunday.
The memorial service is one of the biggest gatherings of international dignitaries in recent years.
There had been fears people would be turned away, but the heavy rain left areas of the 95,000 capacity stadium empty.
Introducing the proceedings, the master of ceremonies, Cyril Ramaphosa, said that Nelson Mandela’s “long walk is over… and he can finally rest”.
The first speaker, friend and fellow Robben Island inmate Andrew Mlangeni, said Neslon Mandela had “created hope when there was none”.
Barack Obama delivered his address, carried on the White House web site, to huge cheers. He said: “It is hard to eulogize any man… how much harder to do so for a giant of history, who moved a nation towards justice.”
He said Nelson Mandela had taught the world the power of action and the power of ideas, and that it had taken a man like Mandela to free not only the prisoner but also the jailer.
Barack Obama said: “We will never see the likes of Nelson Mandela again. While I will always fall short of Madiba [Nelson Mandela’s clan name], he makes me want to be a better man.”
On his way to the podium, Barack Obama shook hands with Cuban President Raul Castro, an unprecedented gesture between the leaders of two nations that have been at loggerheads for more than half a century.
In his address, UN Secretary General Ban Ki-moon said there was “sorrow for a mighty loss and celebration of a mighty life”.
Ban Ki-moon said: “South Africa has lost a hero, it has lost a father… He was one of our greatest teachers. He taught by example. He sacrificed so much and was willing to give up all he had for freedom and democracy.”
Nelson Mandela’s widow, Graca Machel, arrived at the stadium to huge cheers as she was shown on the big screen.
There were cheers too of “Winnie! Winnie!” for ex-wife Winnie Madikizela-Mandela, who hugged and kissed Graca Machel.
However, there were boos for current President Jacob Zuma.
He will make the keynote address. Brazilian President Dilma Rousseff, Chinese Vice-President Li Yuanchao, President Hifikepunye Pohamba of Namibia and Indian President Pranab Mukherjee are also making speeches.
Raul Castro will also speak, reflecting the fact that under his brother, Fidel, Cuba was a staunch critic of apartheid, and Nelson Mandela had expressed gratitude for that support.
The memorial service, which had been due to start at 11:00, will last about four hours, according to the official programme.
Correspondents say that the heavy rain, security and transport issues and the fact that Tuesday was not declared a national holiday have kept the numbers down.
Nelson Mandela’s body will lie in state in Pretoria on the following three days and a state funeral takes place on Sunday in his home village of Qunu in Eastern Cape province.
More than 100 current or former heads of state or government will attend the funeral or the national memorial, according to the South African government.
Among those not attending the memorial events will be Israel’s PM Benjamin Netanyahu, who cited high travel and security costs.
However, there will be suspicion that he wishes to avoid the potential for anti-Israeli protests.
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