US President Barack Obama on Saturday met the family of his "inspiration" Nelson Mandela but was unable to visit the anti-apartheid legend who remains critically ill in hospital.

Despite tentative signs of an improvement in the condition of the father of multi-racial South Africa, Obama decided not to visit Mandela during his visit for fearing of disturbing his "peace and comfort".

Instead Obama met privately with some relatives of the revered leader including two daughters and several grandchildren and spoke by telephone with Mandela's wife Graca Machel.

"I expressed my hope that Madiba draws peace and comfort from the time that he is spending with loved ones, and also expressed my heartfelt support for the entire family as they work through this difficult time," Obama said, using Mandela's clan name.

Machel said she had "drawn strength from the support" offered by the Obama family.

"I am humbled by their comfort and messages of strength and inspiration which I have already conveyed to Madiba."

Speaking earlier in Pretoria, where 94-year-old Mandela lay fighting for his life in a nearby hospital, Obama praised the "moral courage" of South Africa's first black president.

"The struggle here against apartheid, for freedom, Madiba's moral courage, his country's historic transition to a free and democratic nation, has been a personal inspiration to me. It has been an inspiration to the world," Obama said after talks with President Jacob Zuma.

"The outpouring of love that we've seen in recent days shows that the triumph of Nelson Mandela and this nation speaks to something very deep in the human spirit -- the yearning for justice and dignity that transcends boundaries of race and class and faith and country," he added.

Obama said before arriving he did not need "a photo-op" with Mandela, whom he meet briefly in 2005, and the White House on Saturday ruled out a meeting between the two men.

"Out of deference to Nelson Mandela's peace and comfort and the family's wishes, they will not be visiting the hospital," the official said.

Obama's three-nation tour is aimed at changing perceptions that he has neglected Africa since his election in 2008, while also countering China's growing economic influence in the resource-rich continent.

But it has been overshadowed by the illness of his fellow Nobel peace laureate, who has been in intensive care for more than three weeks.

Zuma said Mandela remained in "critical but stable" condition, expressing hope that he would improve.

Welcoming the US president to South Africa on the second leg of his tour, he said Mandela and Obama were "bound by history" as the first black leaders of their respective nations.

"You both carry the dreams of millions of people in Africa," Zuma said.

But the US leader was not greeted so warmly by all South Africans. Riot police fired stun grenades at anti-Obama protesters in the township of Soweto, once a flashpoint in the anti-apartheid struggle.

Mandela's condition presents Obama with a sensitive political challenge.

He must balance a desire to honour Mandela, in perhaps his final days, with a message that the United States wants to play a key diplomatic and economic role in a region on the rise.

Supporters have been gathering outside the Pretoria hospital to offer prayers for the man who negotiated an end to decades of white minority rule.

A wall of handwritten prayers has become the focal point for South Africans paying tribute to the father of their nation, with singing and dancing by day and candlelight vigils at night.

"I'm here this morning to give my prayers. It's important because Mandela is so important to us South Africans and Africans," said Tokozile Sibalo, 50, a receptionist at an Internet company who came with her daughters, 20 and 12.

South Africa's last apartheid president FW de Klerk cut short a visit to Europe because of the ailing health of his co-Nobel prize winner.

Obama's itinerary included a visit to Soweto, the sprawling township where riots sparked a nationwide struggle against the racist apartheid regime, with many residents preparing to welcome the US president as a "fellow African".

"To me, Madiba represents an older and perhaps more traditional generation of black leaders, while Obama represents the new generation," Tshepo Mofokeng, 43, told AFP. "I'm sure he will be welcomed here as an African."

The US leader will hold a town hall-style meeting with young leaders from all over Africa, driving home his theme that it is time for a new generation to guide the continent into a new era of democracy and prosperity.

Mandela may be out of sight, but his influence is palpable on Obama's tour of Senegal, South Africa and Tanzania.

A visit by Obama on Sunday to Mandela's former jail cell on Robben Island, off Cape Town in particular is expected to be laden with symbolism.

Obama will then visit former Archbishop Desmond Tutu's youth foundation HIV centre before delivering the central speech of his African tour at the University of Cape Town.

Mandela has been hospitalised four times since December.

The man once branded a terrorist by the United States and Britain won South Africa's first fully democratic elections in 1994, forging a path of racial reconciliation during his single term as president, before taking up a new role as a roving elder statesman and leading AIDS campaigner.