Nelson Mandela responding to treatment, South president Africa Jacob Zuma says

Updated at 10:45 a.m. ET

JOHANNESBURG South Africa's president said Wednesday that Nelson Mandela was responding better to treatment after several days in the hospital.

President Jacob Zuma told parliament he was happy with the progress that the international icon was making "following a difficult last few days."

Mandela's grandson, Nkosi Zwelivelile Mandela, released a statement after visiting Mandela in hospital Wednesday morning with other members of the family.

In it, he said that the Mandela family is, "Heartened by the overwhelming messages of support from the public."

"For the past few days since Madiba was admitted to hospital, the family has been deeply touched by the outpour of prayers and the overwhelming messages of goodwill from all South Africans and the international community," said Nkosi Mandela.

The family is satisfied with the care that Madiba is receiving and share the hope of everyone for Madiba's recovery.

"We are fully cognizant of the fact that millions of people in the country and around the world regard Madiba as their parent and therefore are as much concerned about his well-being as we are. The family would like to extend our sincere gratitude to the South African government, the African National Congress (ANC) and the doctors in charge of Madiba's health during this period," said Nkosi Mandela.

The statement adds that the family is also happy with the sterling work by the Presidency in keeping the public updated about Madiba's health.

Mandela spent a fifth straight day Wednesday in a Pretoria hospital, where he is being treated for a recurring lung infection. The 94-year-old former president was hospitalized on Saturday.

Zuma's remarks were the first departure from the government's classification of Mandela's condition as "serious but stable," which they had refused to expand on all week.

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The president's statement to lawmakers offered little new insight into Mandela's specific ailments, symptoms, or treatment.

A trusted CBS News source said earlier this week, however, that the ex-leader's liver and kidneys were functioning at just 50 percent capacity, and that he had to be resuscitated before even reaching the hospital on Saturday.

The South African government has not commented on the source's information, first reported Monday night by CBS News correspondent Mark Philips.