Cape Town - The health of former president Nelson Mandela was weighing on Thursday on the visit by US President Barack Obama and an entourage of about 1 000 people to South Africa.
He is due in the country on Friday.
Mandela's condition was on Thursday described by the Presidency as critical, but stable.
The anti-apartheid icon is being treated in Pretoria's Medi-Clinic Heart Hospital, after he was admitted on 8 June with a recurring lung infection.
President Jacob Zuma on Wednesday, after a visit to Mandela, called off a scheduled SADC meeting in Mozambique.
Many took this as a sign that Mandela was now dying - or even already dead, as some reports had it.
However, on Thursday, following his second visit to Mandela's bedside in 24 hours, Zuma reported his condition had improved.
The US diplomats in South Africa are said to be deeply concerned, given what would happen in the event of Mandela's death and the subsequent national mourning.
They know that if Mandela died, the president's agenda, including a keynote speech in Cape Town - probably on the future of Africa - would be impossible.
The ailing leader's grandson, Mandla, said the Nobel Peace laureate's fate "lies with God and our ancestors".
"Every improvement in my grandfather's health is cause for celebration."
A large number of family members gathered at the hospital on Thursday.
"I won't lie. It doesn't look good," daughter Makaziwe Mandela said. But "if we speak to him he responds and tries to open his eyes -- he's still there".
She criticised the media who have besieged the hospital for weeks in tents, caravans and satellite vans, calling foreign journalists "vultures" who were "waiting for the last carcasses".
"There is an element of racism to their attitude.
"That is the image that we have as a family," she said in an SABC interview.
Meanwhile, vigils continue in front of the hospital. Children bring pictures they have drawn, teddy bears, dolls and balloons, while adults lay down bouquets and greeting cards.
The closely guarded hospital is increasingly a place of pilgrimage.
At night, candles burn in front of the hospital. People are often seen praying together. During the day there is a lot of singing.
The fate of the grand old man of South Africa is on everyone's lips. "Let him die with dignity at last," Cape Town businesswoman Glini Le Roux said, articulating what many were thinking.