Zuma issued the statement after visiting Mandela at a Pretoria hospital, where he was admitted June 8 with a recurring lung infection. No further details were provided about Mandela's health.
The news that South Africa's first black president, who is revered for his struggle to end white minority rule, remains in critical condition dampened hopes that he could be sent home soon.
Last week, Mandela's daughter, Zindzi, said he could be released from the hospital at any moment. Other reports said he was able to respond with his eyes and smile at well-wishers who visited him last Thursday on his 95th birthday.
South Africa erupted with love and joy when Mandela celebrated the day in the hospital after weeks when he appeared to be nearing death.
"The president once again assured Madiba of the love and support of all South Africans," Zuma said in Monday's statement, using Mandela's clan name. "The birthday celebrations for the former president on the 18th of July were the biggest ever this year, attracting scores of South Africans who engaged in community service in honor of Madiba."
Zuma reiterated his call to the nation to "continue to keep Madiba in their thoughts and prayers."