A grandson of Nelson Mandela has said the ailing anti-apartheid icon and former president is very much alive, while the South African government announced he remains in a critical but stable condition.

Ndaba Mandela, whose father Magkatho was Mandela's second son with first wife Evelyn Mase, urged well-wishers to celebrate the life of the 94-year-old statesman ahead of his 95th birthday.

Mandela became South Africa's first democratically elected president after spending 27 years in prison for his fight against racist white rule.

"With less than two weeks to go before the old man's birthday, it's time to celebrate his life," Ndaba Mandela said in Pretoria. "The old man is very much alive."

Ndaba Mandela said his grandfather responds when spoken to, mirroring comments made last week by fellow prisoner and lifelong friend Ahmed Kathrada.

"When I speak to him, he responds," Ndaba Mandela said. "Let us not be in a spirit of sadness but a spirit of celebration because the old man is still with us today."

The Presidency said on Tuesday that Mandela was still in a critical but stable condition at the Pretoria hospital where he is receiving treatment for a recurring lung infection.

Court documents revealed last week that he was breathing with the help of a ventilator.

President Jacob Zuma thanked the public for the continued show of support outside the hospital.

"The prayer services around the country are also appreciated," Zuma said in a statement. "We thank the international community as well for ongoing messages of support to Madiba and his family."

Well-wishers from around the world continue to stop outside his Johannesburg home and the Pretoria hospital.