Mandela's family thanked South Africa and the wider world for their support.
"It has not been easy for the last two days and it won't be pleasant for the days to come. But with the support we are receiving from here and beyond, in due time all will be well for the family," they said in a statement.
Ordinary people expressed admiration and respect for the achievements of Nobel peace laureate Mandela, who died on Thursday after a prolonged battle with a lung infection.
Thousands of people across South Africa saluted Nelson Mandela with smiles and moments of silence in honour of the late anti-apartheid leader, who inspired people to pursue the impossible from politics to the playing field.
The tributes stretched across the South African sporting spectrum.
Minutes of silence were observed from club cricket and fun runs to top fixtures such as a League Cup final between Platinum Stars and Orlando Pirates.
The Soweto giants were believed to have been Mandela's favourite soccer side.
Many recalled Mandela's central role in arguably South Africa's greatest sporting triumph - winning the 1995 rugby World Cup just one year after the multi-racial elections that ended decades of white-minority rule.
Mandela then followed up with a political masterstroke, bridging the gulf between white and black by appearing in a dark green Springbok jersey, a sporting strip enmeshed in the then-entrenched culture of white supremacy.
Preparations are under way for a week of national mourning, culminating in Mandela's burial on 15 December at his ancestral home in Qunu in the Eastern Cape Province, 700km south of Johannesburg.
A State Memorial Service for the former South African President will take place in Johannesburg on Tuesday.
The remains of the 95-year-old will lie in state in Pretoria from Wednesday to Friday of next week.
He will then be flown to his ancestral home of Qunu in the Eastern Cape for a State funeral on Sunday week.
Hours after President Jacob Zuma announced the 95-year-old's death, South Africans of all races took to the streets and the Internet to express sorrow at his passing and celebrate his remarkable life.
Former President FW De Klerk, the last white president who help dismantle the apartheid system of institutionalised racism, said Afrikaners had "very warm feelings towards Nelson Mandela" and would mourn him.
While the death of anti-apartheid leader Nelson Mandela triggered an outpouring of shared sorrow across South Africa's sometimes tense racial divide, eyes stayed dry in a white Afrikaner enclave in the heart of the country.
In Orania, where a small community of 1,000 Afrikaners has closed itself off, intent on preserving its culture and language at all cost, the global icon who preached a contrasting ideology of racial integration commands respect.
Mandela, who became South Africa's first black president in 1994 after spending 27 years in jail for fighting white rule, astounded Orania's residents when he visited the settlement the following year as a gesture of conciliation.
The image, published in papers across the world, of the towering Mandela with his arm around the widow of apartheid architect Hendrik Verwoerd after the two shared tea, cemented his stature as one of the world's most respected statesmen.
The visit triggered mixed emotions, including anger from some black and white South Africans.
But 18 years later, the memory appears to have faded from this self-contained community, which shuns contact with the outside world to the point of having its own currency, the Ora.
"I don't really know much about him," one elderly woman said when asked about Mandela's death, before quickly walking away, reflecting the suspicion that greets any visitor, especially a non-white reporter.
Residents deny charges of racism, but remain uneasy about life in a South Africa led by a black-majority government after decades of white minority rule.
Irish response hailed
The South African Ambassador to Ireland has described the response of Irish people to the death of Nelson Mandela as "amazing".
Jeremiah Ndou said South Africans had been humbled by the messages of support following the death of the former president.
The ambassador said he was expecting a huge turnout at a memorial service planned for St Patrick's Cathedral, Dublin on Thursday.
The Irish branch of Mr Mandela's ANC party is also organising a service tomorrow evening at the AFM Promise Tabernacle, St Michans Street, Dublin.
Books of condolence for Mr Mandela are now open across the country.
In Dublin, a book of condolence can be signed at the Mansion House today and tomorrow and also at St Patrick's Cathedral from today until this day week.
Books of condolence are also being made available in Cork, Limerick, Galway and Belfast.
Dunnes Stores anti-apartheid strike
More than half of those who took part in the Dunnes Stores anti-apartheid strike are expected to travel to South Africa for the funeral services of Nelson Mandela.
The Irish Government has invited one of the activists to attend as part of the official State delegation.
Trade union Mandate is arranging for other members of the group to travel to South Africa for the memorial events.
Dunnes Stores workers were turned away by armed guards when they originally visited South Africa in 1985.
Former shop steward Karen Gearon said: "As we were going back on the plane (in 1985) I turned around and put my fist up and said 'we will be back when South Africa is free.' And we are going back, and South Africa is free."
The strikers thanked those who had campaigned for them to attend the funeral.
Former trade union official, Brendan Archbold said: "This really wasn't on the cards at all but things have developed very quickly in the last 24 hours."
"This is international solidarity at its best".
The Tánaiste and Minister for Foreign Affairs, Eamon Gilmore, also is expected to travel to Johannesburg for the service.