Spokesperson Mac Maharaj said Mandela's situation was serious but stable.
Maharaj told eNCA on Saturday that doctors had confirmed Mandela was breathing on his own.
"That is a good sign, I think," Maharaj said.
"This morning at about 1.30am his condition deteriorated and he was transferred to a Pretoria hospital," presidency spokesperson Mac Maharaj said in a statement.
"He remains in a serious but stable condition."
Maharaj said doctors were doing everything they could to make Mandela "better and comfortable".
"President Jacob Zuma, on behalf of government and the nation, wishes Madiba a speedy recovery and requests the media and the public to respect the privacy of Madiba and his family," Maharaj said.
Mandela's wife, Graca Machel, has been by his side since being admitted to hospital.
On April 6, Mandela was discharged from hospital after spending nine days receiving treatment for a recurring lung infection. The Nobel Peace Prize laureate has suffered lung ailments before and has been in and out of hospital.
Regular hospital stays
Early in March, he was admitted to a Pretoria hospital for a scheduled check-up and was discharged the following day.
In December last year, Mandela underwent an operation to remove gallstones and treat the recurring lung infection. He was discharged after an 18-day stay and placed under home-based high care at his Houghton home in Johannesburg.
In January, the presidency said Mandela had made a full recovery from surgery and continued to improve. In February last year he was admitted to hospital for a stomach ailment.
At the time, the presidency said Mandela underwent a diagnostic procedure to investigate the cause of a long-standing abdominal complaint.
In January 2011, Mandela was taken to Milpark Hospital for routine tests relating to respiratory problems.
Mandela's last major public appearance was in July 2010, at the final of the Fifa World Cup at Soccer City stadium in Johannesburg.
Since then he had spent his time between Johannesburg and his ancestral village of Qunu in the Eastern Cape.
The African National Congress and its alliance partners have wished Mandela a speedy recovery.
"We send to him our well wishes for a speedy recovery so that he may soon be discharged to return to the care and comfort of his home," ANC spokesperson Jackson Mthembu said in a statement.
Mthembu said: "The ANC hopes and trusts that president Mandela and his family will be afforded the necessary respect and privacy while he is in hospital, we have no doubt that Tata will continue to receive expert medical care and attention at this time."
The Congress of South African Trade Unions said its members were keeping Madiba in their thoughts.
"Our 2.2-million members, thousands of working people, millions of South Africans and countless more freedom-loving people around the world are thinking of you today and wishing that you make a full recovery and soon return home," the trade union federation said in a statement.
The South African Communist Party sent its support to Mandela's family.
United Kingdom Prime Minister David Cameron sent Mandela well wishes on Twitter.
"My thoughts are with Nelson Mandela who is in hospital in South Africa," Cameron tweeted.
Home town shock
Residents from the small Eastern Cape village of Qunu were shocked after hearing of Mandela's hospital admission.
Malunga Mbokodi (62) who lives 1km from Mandela's Qunu home said he was shocked when he heard the news on the radio.
"I was shocked to hear from the radio this morning [Saturday] that he was again in hospital," Mbokodi said.
"But again we cannot trust the media because last time the media was reporting wrongly, saying Mandela was in hospital, while the government said he was not in that hospital, so who do you believe.
"I think, we should just accept it that Mandela is old and he will go soon."
The Mandela family in Qunu were waiting for Mandla Mandela, the elder statesman's grandson, to arrive at the Mvezo royal palace.
Mandla was expected to brief the Mandela elders on the latest developments concerning his grandfather.
One of the Mandela family elders, Napilisi Mandela said he received news of Mandela's hospitalisation this morning.
"I must say Mthembu, I was shocked that Dalibhunga is back in hospital … I am here in Mvezo waiting to meet Mandla, who I believe is now journeying from Mthatha," Napilisi said.
Media had started gathering in Qunu.
A few reporters had positioned themselves outside keeping a careful watch on the Mandela residence.
Well wishes from the youth
Young South Africans have also wished Madiba a speedy recovery.
"Tata get better. We are going to pray for you," Gail Prosperity (22) said.
She said she only found out Mandela was in hospital after she saw the large media contingency outside the hospital.
"Honestly I don't want to lie to you it really touched me … My spirit is going down.
"This thing for Madiba is inside of us."
Prosperity said she wanted him to get well soon as he gave South Africa freedom.
Runs Mabuza (31) who lives opposite the hospital said he was feeling bad about Mandela's hospitalisation.
"He's sick and then he is old. The country loves him," he said.
"I wish him the best and that he must recover quickly."
A group of journalists, armed with cameras, are parked around the corner of Mandela's home.
One motorist who was amazed by the media contingent stopped to ask which house was the Mandela residence.
"I've passed here many times before but I've never known which house it is," she said.
Media are also stationed outside the Pretoria hospital with photographers and journalists monitoring cars entering and exiting the hospital.
There was no security apart from normal hospital guard stationed outside the building. – Additional reporting by Sapa