Mandela, 94 and frail, spent his fifth day in a Pretoria hospital Monday after "a restful day" Sunday in which doctors "reported a further improvement in his condition," President Jacob Zuma's office said in a statement.
The statement did not say how much longer doctors expected the anti-apartheid icon and Nobel Peace laureate to stay in the hospital.
Churches across the country held Easter Sunday prayers for Mandela, who is held in deep respect as the "Father of the Nation" and a moral beacon, despite withdrawing from public life almost a decade ago.
Zuma thanked South Africans for praying for Mandela.
"We also thank all people at home and around the world, who continue to keep Madiba and his family in their thoughts and to show their love and support in various ways," he said. "We also thank foreign governments for their messages of support."
Mandela is often spoken of in South Africa by his Xhosa clan name of Madiba. Clan names are often considered more important than surnames among Xhosa people.
Mandela -- South Africa's first black president, elected in 1994 after being released from prison, where he spent 27 years for his efforts to end white rule -- contracted tuberculosis in the 1980s while imprisoned on Robben Island.
He was held on the windswept island off Cape Town for 18 of the 27 years he was imprisoned before apartheid was ended.
His lungs are believed to have been damaged while working in a prison quarry, the BBC said. This latest hospitalization is his fourth in two years.
He was hospitalized for a respiratory infection in January 2011, then for a recurring lung infection in December 2012, where he also had gallstones surgically removed.
He underwent a successful scheduled medical procedure in early March.