Mandela, who turns 95 on July 18, remained "critical but stable" on the 25th day of his hospitalisation for a recurring lung ailment.
To mark the upcoming birthday of the democracy icon, the government appealed to citizens to make the occasion the "biggest Mandela Day ever on the 18th of July, focusing on doing good all over the country."
The theme for Mandela Month 2013 has been declared to be "Take Action, Inspire Change. Make Every Day a Mandela Day."
"To celebrate Mandela Month, South Africans need to uphold Madiba's ideals, including his unwavering commitment to justice, equality and a non-racial South Africa," Williams added.
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In 2010, the UN General Assembly declared July 18 as Nelson Mandela International Day.
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.