Mr Mandela’s spokesman Mac Maharaj said his condition had deteriorated “in the past 48 hours”.
South Africa’s first black president has been in hospital since 8 June with a recurring lung infection.
Doctors were doing everything to ensure his well-being, a statement said.
On Tuesday, a cleric prayed for Mr Mandela’s “peaceful end”.
Also visiting on Tuesday was Mr Mandela’s daughter Zindzi, who said her father had “opened his eyes and smiled”.
Gratitude
The statement from his office said he “reiterated his gratitude on behalf of government, to all South Africans who continue to support the Madiba family”.
President Zuma’s decision to cancel the visit to Mozambique where he was to attend a regional infrastructure investment conference further underlines the gravity of Nelson Mandela’s condition, the BBC’s Mike Wooldridge reports from Johannesburg.
Mr Mandela, known by his clan name Madiba, is revered for leading the fight against white minority rule in South Africa and then preaching reconciliation despite being imprisoned for 27 years.
He was awarded the Nobel Peace Prize in 1993 and was elected president the following year. He left office in 1999 after a single term.
Mr Mandela retired from public life in 2004 and has rarely been seen at official events since.
He has a long history of lung problems, and was diagnosed with tuberculosis in the 1980s while he was a prisoner on Robben Island.
After his release, Mr Mandela said that the tuberculosis was probably caused by dampness in his prison cell.