Mandela's eldest daughter Makaziwe, however, warned that her father, who was hospitalised 20 days ago for a recurring lung ailment, was "very critical" and "anything is imminent".
As the eyes of the world remain fixed on the health condition of the 94-year-old peace hero, Zuma said Mandela's medical team told him that the former president "remains critical but is now stable."
Mandela's "condition has improved during the course of the night," Zuma said in a statement after visiting him for a second time in 24 hours in the Mediclinic Heart Hospital in Pretoria.
He also urged people to refrain from spreading rumours about the democracy icon's medical condition.
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Earlier, Makaziwe said her father was opening his eyes and still reactive to touch.
"But I want to emphasise again that it's only God who knows when the time to go is and so we will wait with him, with Tata, as long for us as a family, he's still giving us hope opening his eyes he's still reactive to touch we will live with that hope until the final end comes," she said.
Mandela, respected across the globe as a symbol of resistance against injustice, had a long history of lung problems, dating back to the time when he was a political prisoner on Robben Island during apartheid.
Mandela is revered for leading the fight against white minority rule in the African country and then preaching reconciliation despite being imprisoned for 27 years.
Mandela, regarded the founding father of South Africa's multiracial democracy, served as the country's first black president from 1994 to 1999.
He left power after five years as president.
Mandela was awarded the Nobel Peace Prize in 1993.
He retired from public life in 2004 and has not been seen in public since the football World Cup finals in in 2010.
Mandela turns 95 on July 18.