Barack Obama led world tributes to Mandela, hailing him as "a giant of history" and comparing him to Mahatma Gandhi, Martin Luther King and Abraham Lincoln.

He said: "It is hard to eulogise any man ... how much harder to do so for a giant of history, who moved a nation towards justice."

Obama pointed out that "around the world today, men and women are still imprisoned for their political beliefs; and are still persecuted for what they look like, or how they worship, or who they love".

Before taking to the stage, Obama shook hands with Cuban leader Raul Castro.

The greeting between the leaders of long-time cold war foes was seen by millions around the world in the live broadcast of the ceremony.

It was only the second time since diplomatic ties were broken in 1961 that leaders of the two countries have greeted each other - and it was the first time the greeting has taken place in public.

Cuban leader Fidel Castro and Bill Clinton exchanged greetings in 2000 during the Millennium summit in New York. There was no picture of the encounter.

UN Secretary General Ban Ki-moon noted that Mandela had managed to unite people in death, much as he had in life.

"Look around this stage ... we see leaders representing many points of view ... all here, all united," he said.

In a display of Mandela's extraordinary global reach, popularity and influence, the Indian, Brazilian and Namibian presidents, as well as Castro, delivered eulogies.

China was represented by Vice-President Li Yuanchao , who said: "Mandela was the pride of the African people. He dedicated his entire life to the development and progress of the African continent."

The crowds booed South African President Jacob Zuma, who gave the keynote address at the service. Many South Africans are unhappy with Zuma because of state corruption scandals.

Thabo Mbeki, the former South African president who succeeded Mandela, got a rousing cheer as he entered the stands.

Mandela's widow, Graca Machel, received a huge ovation as she took her seat. She gave Mandela's former wife Winnie Madikizela-Mandela a long hug before the ceremony began.

Yesterday was also the 20th anniversary of the day when Mandela and South Africa's last apartheid-era president, F.W. de Klerk, received the Nobel Peace Prize.

De Klerk, a political rival who became friends with Mandela, was also present in Soweto's FNB stadium.

Steady rain kept many people away. The 95,000-capacity stadium was two-thirds full as the ceremony got under way.

Some of the dozens of trains laid on to ferry people to the stadium were delayed due to a power failure.

A traffic jam also delayed Obama, who missed the first hour of the ceremony as his motorcade struggled along the route to the stadium. Some had started gathering before daybreak to secure a seat at the venue. Wrapped in the South African flag or yellow-green coloured shawls printed with the slogan "Mandela Forever", they danced and sang - oblivious to the constant drizzle.

"He's God given, he's God taken. We will never stop cherishing Mr Mandela," said Shahim Ismail, who took a day off work to attend the event.

"This is history," said Noma Kova, 36. "I didn't want to watch this on television."

Screens were set up in three other stadiums in Johannesburg to allow 200,000 people to watch the memorial service.

"In our culture the rain is a blessing," said Harry Tshabalala, a driver for the justice ministry. "Only great, great people are memorialised with it. Rain is life. This is perfect weather for us on this occasion."

The stadium was also where Mandela made his last public appearance at the closing ceremony of the soccer World Cup.

Mandela's body will lie in state for three days at the Union Buildings in Pretoria, once the seat of white power, before burial on Sunday in his rural childhood village of Qunu in Eastern Cape Province.