Nelson Mandela is in intensive care with his wife by his side, but his condition has not changed.
Mandela was in serious but stable condition in a Pretoria hospital for the third day on Monday (local time) with a recurring lung infection.
As family members visited South Africa's first black president in the hospital, the government announced - in only the second communication on Mandela since he was hospitalised on Saturday - that his condition was "unchanged".
Mandela was visited by his former wife Winnie Madikizela-Mandela and their daughter Zindzi. The former president’s two other daughters paid him a visit on Sunday, while his current wife Graca Machel has been by his bedside since his admission to hospital.
A statement issued for the Desmond and Leah Tutu Legacy Foundation described Mandela as "the beloved father of our nation" and offered prayers for a man seen by many around the world as a symbol of reconciliation because of his peacemaking role when white racist rule ended in South Africa.
Mandela "once again endures the ravages of time in hospital", said the Cape Town-based foundation, which was founded by Tutu and his wife Leah to promote peace. "We offer our thanks to God for the extraordinary gift of Mr Mandela, and wish his family strength."
Tutu, 81, was also vigorous campaigner against apartheid, which ended when all-race elections were held in 1994 and Mandela president. Like Mandela, Tutu was awarded the Nobel Peace Prize for his efforts on behalf of his compatriots. Mandela shared his prize with FW de Klerk, the last president of the apartheid era.
"We send our blessings to the doctors and nurses responsible for his care," Tutu's foundation said.
Meanwhile, the African National Congress, South Africa's ruling party, dismissed as false a report in Monday's edition of The Star newspaper that Mandela's family had barred senior party leaders and government officials from visiting the hospital.
On April 29, state television broadcast footage of a visit to Mandela's home by President Jacob Zuma and other ANC leaders. Zuma said then that Mandela was in good shape, but the footage - the first public images of Mandela in nearly a year - showed him silent and unresponsive, even when Zuma tried to hold his hand.
Some South Africans said that showing images of a clearly ill Mandela was inappropriate and appeared to reflect an attempt by the ruling party to benefit politically from its association with Mandela, a former ANC head, in the run-up to national elections next year. The party denied the accusation.
In its brief statement on Mandela's health, the presidency said Zuma "reiterates his call for South Africa to pray for Madiba and the family during this time", referring to Mandela by his clan name.
Mandela has been hospitalised several times in recent months. During a hospital stay that ended April 6, doctors diagnosed him with pneumonia and drained fluid from his chest.
Mandela has been particularly vulnerable to respiratory problems since contracting tuberculosis during 27 years as the prisoner of the white racist government. The bulk of that period was spent on Robben Island, off the coast of Cape Town where Mandela and other prisoners spent part of the time toiling in a stone quarry.
He was freed in 1990, and then embarked on peacemaking efforts during the tense transition that saw the demise of the apartheid system and his own election as president in 1994.
The former leader retired from public life years ago and had received medical care at his Johannesburg home until his latest transfer to a hospital.