World leaders from around 90 countries, along with tens of thousands of South Africans, have paid their tributes to Nelson Mandela at a memorial service in Johannesburg, recalling the iconic former president's contributions for reconciliation across political and racial divides.

In his address at the ceremony at Johannesburg's Soccer City Stadium on Tuesday, US President Barack Obama called Mandela, who died last Thursday at the age of 95, the "giant of history" and described him as a leader who "moved a nation towards justice".

Speaking under rain on Tuesday, Obama said that Mandela earned his place in history through struggle, shrewdness, persistence and faith, comparing him to Mahatma Gandhi, Martin Luther King Jr. and Abraham Lincoln. "There are too many leaders who claim solidarity with Madiba's [Mandela's clan name] struggle for freedom, but do not tolerate dissent from their own people," he said, stabbing his finger in the air.

"Nothing he achieved was inevitable. In the arc of his life, we see a man who earned his place in history through struggle and shrewdness, persistence and faith.”

Zuma booed

Jacob Zuma, the South African president, was booed and jeered before his speech at the memorial in a major public humiliation in front of leaders six months before national elections. Many South Africans in the ten-thousands-strong crowd emptied their seats of the stadium during his address.

Zuma said that everyone had a Madiba moment in their life as Mandela "touched their lives".

"That we are Madiba's compatriots and that we lived in Madiba's time is a reason for great celebration," he said.

At a landmark moment at the ceremony, Obama shook the hand of Raul Castro, leader of long-time Cold War foe Cuba, in an unprecedented gesture between the leaders of two nations which have been at loggerheads for more than half a century. Castro smiled as Obama shook his hand on the way to the podium to make his speech at the commemoration.

'Unjust punishment'

In his speech, Raul Castro quoted his brother Fidel Castro, former Cuba leader, and said, "Mandela will not go down in history for the 27 years he spent behind bars... but because he was able to free his soul from the poison that such unjust punishment can cause."

Coinciding with UN-designated Human Rights Day, the memorial service for Mandela was the centrepiece of a week of mourning for the globally-admired statesman. Singing joyous crowds were all around around the stadium despite the rain.

Australian Prime Minister Tony Abbott, French President Francois Hollande, German President Joachim Gauck, Canadian Prime Minister Stephen Harpe, Spanish Prime Minister Mariano Rajoy, Brazilian President Dilma Rousseff, Indian President Pranab Mukherjee, European Commission President Jose Manuel Barroso and European Union Council President Herman Van Rompuy were among the participants of the memorial.

Robert Mugabe, the Zimbabwean president, and Tony Blair, the former British prime minister, also attended the ceremony, an indicator of many that hostilities were put on hold for the day. Blair has called Mugabe a dictator who should have been removed from power. Mugabe has called Blair an imperialist and once told him to "go to hell".

Ban Ki-Moon, the United Nations Secretary-General who was also attending the ceremony, said: "He [Mandela] has done it again.... We see leaders representing many points of view, and people from all walks of life. All here, united... He showed the awesome power of forgiveness and of connecting people with each other."

Israel's top leaders have been conspicuous by their absence at the memorial, skipping the ceremony for the anti-apartheid icon whom Palestinians have always viewed as their comrade in the struggle for freedom. Neither Prime Minister Benjamin Netanyahu nor President Shimon Peres attended the event.

A procession in Pretoria on Wednesday will mark the start of a three-day lying in state, to give ordinary South Africans the chance to say a final, personal farewell to Mandela.

The government has encouraged the public to turn out in force and line the route from the city's 1 Military Hospital to the Union Buildings where he was sworn in as their first black president nearly 20 years ago.