Visitors, including top ANC officials, continued to flock to the Milpark Hospital here for a second day as Nobel Laureate Mandela, 92, remained under observation for "routine tests", as stated by his Foundation.
President Jacob Zuma called for calm as the nation awaited updates on the ailing leader`s condition.
"President Mandela is comfortable and is well looked after by a good team of medical specialists," Zuma said in a statement from Davos, from the World Economic Forum meet.
"We urge the media to afford him the dignity and respect that he is entitled to as the country`s founding democratic president, as a national hero and also as a citizen of the republic."
The ruling ANC party called for calm, urging South Africans "not to press any panic buttons".
"We call on all South Africans to remain calm regarding the hospitalisation of Madiba and not press any panic buttons, as there is no reason for that whatsoever," ANC spokesman Jackson Mthembu said.
"If there is any change in the hospitalisation of Madiba, including his discharge from hospital, (it) will be communicated."
South Africans prayed for the health of anti-apartheid hero Nelson Mandela as children at a local school have hung messages of support outside the Milpark Hospital.
The democracy icon - known affectionately among South Africans by his clan name, Madiba - has appeared increasingly frail on his infrequent public appearances since retiring from public life in 2004.
His last public appearance was at the football World Cup closing ceremony last July. Privately his friends have warned that his health has begun to deteriorate more rapidly in recent months, according to the BBC.
Several of Mandela`s family members, including his wife Graca Machel, were seen visiting the hospital on last night.
In a statement, the Nelson Mandela Foundation insisted Mandela was "in no danger and is in good spirits". It said he was undergoing routine tests, though South African media report he is being seen by a lung specialist.
Earlier rumours had started on social networks that Mandela was very ill, some even declaring that the leader had died.
Neither the Mandela family nor the hospital would provide any details of what was ailing the iconic leader who led South Africa to democracy.
The only official statement was a brief one from the Nelson Mandela Foundation, which said Mandela was "in no danger and in good spirits."
ANC spokesperson Brian Sokhutu said that some senior leaders of the ANC would shortly visit Mandela after consulting the family as he repeated a call to South Africans to avoid undue panic about the leader`s health.
A spokesman for President Jacob Zuma, who was in Davos at the World Economic Forum, said he had no plans to return early in view of Mandela`s hospitalisation.
A huge contingent of local and foreign media has been camping out at vantage points on the periphery of the hospital, especially on a motorway bridge overlooking the facility.
Local police removed them from the bridge, yesterday, citing danger to themselves and passing motorists.
Thorough checks are also being conducted on vehicles entering the hospital premises, including examining the trunks for possible hidden journalists trying to sneak into the hospital.
Social networks are being flooded with messages of goodwill for Mandela, with a poignant message from his granddaughter Zoleka Mandela on Facebook being widely circulated.
"I really hate to see you this way. It kills me each time. Know that I`m here for you as I believe you have always been for me. We are all with you every step of the way.
Spending my next few days with you just so I know that you`ll be OK. I`m saddened," read the message.
Mandela served as President of South Africa from 1994 to 1999, and was the first South African president to be elected in a fully representative democratic election.