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He was giving the team a final send-off at the presidential guest house in Pretoria on Thursday evening.
The Olympic Games take place from July 27 to August 12, and the Paralympic Games from August 29 to September 9.
"Team South Africa, now is your turn to take this nation to even greater heights," Zuma told the athletes.
"We have been to Beijing and now going to London and you must do better than in Beijing."
Sporting a team South Africa tracksuit, Zuma said the athletes had to build on South Africa's past sport successes.
"We successfully hosted the Rugby World Cup in 1995 and won it magnificently. We hosted the Africa Cup of Nations in 1996 and conquered on that occasion," he said.
"We successfully organised the 2010 Fifa Soccer World Cup: hosted thousands of foreign soccer lovers in a month-long football festival."
Zuma said this had proved Africa's capabilities to the world and had challenged the negative stereotypes about the continent.
He said it was the teams' responsibility to not only represent the country, but also the continent, and made it clear that he and the country had great expectations.
"In sport there must be a loser, there must be a winner, all I'm saying is we should be the latter."
Zuma said the team should dedicate the Games to former President Nelson Mandela.
"Win for South Africa and for Africa, and perhaps as important as the others, win for Nelson Mandela, who is turning 94-years-old on July 18.
"He laid the foundation for a winning nation in 1994. We are a winning nation and I can tell you we are going to win," he said.
Zuma shared five values with the athletes which he felt they had to demonstrate when they flew the national flag.
"There are some important values for you to remember as representing the country.
"These are discipline, passion, commitment and dedication. If we have these elements the chances of losing is very far.
"One of them is confidence. This will propel you to greater heights and I am sure you are physically right."
He said it was expected of the athletes to remain drug-free and to refrain from "hectic partying".
"We will be behind you as a nation waving our beautiful rainbow flag at every available moment," he said.
"We want at least 12 medals, not less."
