Jordaan addressed the two squads prior to their departure for Brazil at OR Tambo International Airport in Johannesburg on Saturday.
Vera Pauw's Banyana will start their campaign against Sweden on August 3, a day before Owen da Gama's men face Brazil in their Group A opener.
Jordaan said: "I watched the Banyana Banyana match against the USA at Soldier Field in Chicago, I know the venue very well because it was a 1994 FIFA World Cup Stadium. You must look at your performance on the day, it shows you can play against the best in the world because you really performed very well. We have no fears for you, so you must not have any fear. You must know that you can play against the best and I hope you have already convinced yourselves about that. Those teams that you will meet, you can match them and beat them.
"The end in this tournament is marginal – it is who makes the mistakes, who takes the opportunity because all the teams, including the U-23s, you have gone through a grueling process of qualification and sometimes you forget that you were up against better teams as opposed to the teams that have qualified – so we are already amongst the best teams in the world.
"The Olympics is not an U-23 tournament anymore, for you (Banyana Banyana) there is no age restriction and for the men’s team even that reference is not correct because some of the well-established world players are in the teams, and that indicates to you that all the football countries in the world want to win either the world cup or the gold medal in the Olympics - those are the two things that players and countries want to win. So you will find that countries will put their best players in the teams over the age of 23, and why do they do that, because if it was an age-category tournament they would not have done that – they want to win Olympic gold. That is what the late Muhammad Ali wanted to win, the Olympic gold, every athlete in the world wants that Olympic gold.
"So you must also know that Nigeria, the only African team that went to the 1996 Olympics in Atlanta, all of them became household names. After 1996, that Nigerian team immediately qualified for the 1998 FIFA World Cup in France - Sunday Oliseh, Jay Jay Okocha, that generation of players.
"The Cameroon youth team won the Olympics in Sydney in 2000 and immediately qualified for the 2002 FIFA World Cup in Korea/Japan and so there are two things for this team: to play the Olympics but also to build a team of sufficient quality and strength to qualify for Russia in 2018. So as you play against those players in Rio, you must know you are going to see the same players in Russia in 2018. Same with Banyana Banyana, your next target is the World Cup (2019 in France) – so many of the players you will face here you will meet them in the end at the World Cup.
"This (the Olympics) is the next level of test for any nation and if you succeed at this level, our future at the World Cup for both teams, is almost guaranteed. So you play, focusing on getting out of your group first, don’t try and win in your first match, try and get out of your group first.
"And mostly in these tournaments, as you saw recently in the Euro 2016 finals, the goal of the teams was to get out of the group and once you are in the knockout phase of the competition all hell broke loose there. And teams that were seen as minnows, Iceland, Wales shocked the football world – in any case there are no more minnows anymore in football, there are teams, regardless of the names of players, that go with commitment, passion and team determination that starts fighting when the whistle blows at the start of the match, and stops when the referee says it's over. Those are the teams that win.
"Those years you used to rattle a whole list of players’ names like Romario, Bebeto, Aldair, Ronaldo, Rivaldo and many others - very few teams in the world can rattle those names. But teams that succeed are teams that play as a team, work together, and have the passion and the will to win, and that is what we hope for you. We hope that you go there and show the commitment and make us all proud.
"I just want to wish you all the very best because for many of you, it’s actually launching your own careers on probably the second-highest level of football in the world. You can launch at the World Cup or at the Olympics and if you play well there, you will come back and enter a different world, a different level of football.
"But for now focus on the team, and play with the team, play as a team, win as a team, eat together as a team, carry the pain together as a team, enjoy the celebration, the victory and success as a team, and that is what we ask of you. You have come a long way and worked very hard, and I must say the progress has been phenomenal. I must say this team has grown in stature so I am comfortable that we send two teams that are well prepared, with a lot of quality – now we just wait for the first whistle to blow.
"Again I want to wish you all the best. Congratulations again, you are going to represent us at the Olympics, we are proud of you and we will be watching you.”
SA U-23 Men’s Olympic Fixtures:
Thursday 4 August
Brazil vs SA - 4 Aug
Mane Garrincha Stadium
16h00 (21h00 SA Time)
Sunday 7 August
Denmark vs South Africa
Mane Garrincha Stadium
19h00 (02h00 Monday, 8 Aug SA Time)
Wednesday 10 August
South Africa vs Iraq
22h00 (03h00 Thursday, 11 Aug SA Time)
Banyana Banyana Fixtures for 2016 Olympics:
Wednesday 03 August
Sweden vs South Africa
13h00 (18h00 SA Time)
Saturday 06 August
South Africa vs China
19h00 (12h00 midnight SA Time)
Tuesday 09 August
South Africa vs Brazil
Amazonia Arena (Manaus)
21h00 (02h00 Wednesday, 10 Aug SA Time)