* Ex-wife Winnie says "great improvement" in his condition
* Obama says does not need "photo op" with ailing statesman
* Pretoria protesters burn U.S. flags, slam Obama policies
* Obama due to tour Mandela's old prison during visit
By Peroshni Govender
PRETORIA, June 28 South Africa's ailing anti-apartheid hero Nelson Mandela is doing much better in hospital, his ex-wife Winnie said on Friday before a visit by U.S. President Barack Obama that will include a personal homage to the globally admired statesman.
The faltering health of the first black president of South Africa, a revered symbol of racial reconciliation, has drawn world attention since the 94-year-old was rushed to hospital with a recurring lung infection nearly three weeks ago.
Earlier this week, the government reported Mandela's frail condition had turned critical, but since Thursday President Jacob Zuma has reported that his health is improving.
"I'm not a doctor, but I can say that from what he was a few days ago, there is great improvement," Mandela's ex-wife, Winnie Madikizela-Mandela, told reporters outside Mandela's former home in the Johannesburg township of Soweto.
But, she added, he remained "clinically unwell".
Heading for Johannesburg aboard Air Force One from Senegal, Obama paid tribute to Mandela for the way he led South Africa out of apartheid after years of struggle, but he said he did not need a "photo op" with the former president.
During his weekend trip to Johannesburg, Pretoria and Cape Town, his second stop of a three-nation Africa tour, Obama is scheduled to visit Robben Island, where Mandela passed 18 of the 27 years he spent in apartheid prisons.
White House officials have said they will defer to the Mandela family on whether a visit to the hospital to see Madiba, as he is affectionately known, would be appropriate.
While well-wishers and journalists crowded outside the hospital in the capital Pretoria where Mandela is being treated, a few blocks away, hundreds of demonstrators protested against Obama's visit, some burning U.S. flags.
Nearly 1,000 trade unionists, Muslim activists and South African Communist Party members marched to the U.S. Embassy shouting slogans denouncing Obama's foreign policy as "arrogant and oppressive".
Muslim activists held prayers in a car park outside the embassy. Leader Imam Sayeed Mohammed told the group: "We hope that Mandela feels better and that Obama can learn from him."
South African critics of Obama have focused in particular on his support for U.S. drone strikes overseas, which they say have killed hundreds of innocent civilians, and his failure to fulfil a pledge to close the U.S. military detention centre at Guantanamo Bay in Cuba housing terrorism suspects.
Protesters said the first African-American president should not try to link himself to the anti-apartheid figure.
"Mandela valued human life ... Mandela would condemn drone attacks and civilian deaths, Mandela cannot be his hero, he cannot be on that list," said Yousha Tayob.
"TWO GREAT MEN"
Not far away at the Pretoria heart hospital, some of the people paying tribute to Mandela had words of praise for Obama, who met Mandela in 2005 when he was still a U.S. senator.
Nigerian painter Sanusi Olatunji, 31, had brought portraits of both Mandela and Obama to the wall of the hospital, where flowers, tribute notes and gifts for Madiba, as Mandela is affectionately known, have been piling up.
"These are the two great men of my lifetime," he said.
"To me, Mandela is a prophet who brought peace and opportunity. He made it possible for a black man like me to live in a country that was only for whites."
Obama, in office since 2009, is making his first substantial visit to Africa following a short trip to Ghana at the beginning of his first term.
South Africans held prayer vigils outside the Pretoria hospital and at Mandela's former Soweto home Thursday night.
As his health has deteriorated this year, there is a growing realisation among South Africa's 53 million people that the man who forged their multi-racial "Rainbow Nation" from the ashes of apartheid may be nearing his end.
The possibility of his dying has already generated controversy among the extended Mandela clan.
A dispute between factions of the family over Mandela's proposed final resting place in the Eastern Cape went legal on Friday when his eldest daughter and a dozen other relatives won a court order against his grandson, Mandla.
SABC, South Africa's state broadcaster, said the court had ordered Mandla to return the remains of three of Mandela's children from Mvezo, where Mandla is now chief, to Qunu, Mandela's ancestral home 20 km (13 miles) away.