His ex-wife Winnie Mandela and the couple's daughter Zindzi visited the Pretoria hospital where the 94-year-old is being treated.
Mandela's grandson said he hoped the former South African leader would "recover steadily" but the country's president Jacob Zuma changed tact and told a nation that doctors were doing everything they can to make him comfortable.
ITV News Africa Correspondent Rohit Kachroo said: "There has been a definite change in the tone of the language emerging from the South African government over the last 24 hours or so.
"This is surely an attempt by officials to prepare the nation for this inevitable moment.
"Nelson Mandela's mortality is not in question of course, but clearly the death of such an icon would be a major moment for this country.
"Yesterday there were no references, as there have been in the past, to Mandela's recovery - only a reference to his comfort in hospital.
"As well as anxiety there is also a great deal of anger here about the fact that Mandela's ambulance broke down as he was brought to the hospital a little more than two weeks ago."
Mandela's daughter Makaziwe said the family was taking each day as it came and were enjoying as much time as possible with the anti-apartheid leader.
– Makaziwe speaking to CNN
He is at peace with himself. He has given so much to the world. I believe he is at peace.
Madiba, as he is affectionately known, was the architect of South Africa's 1994 transition to multi-racial democracy after three centuries of white domination.