World Rugby chairman Bill Beaumont hailed a "fantastic" six days as the curtain fell on rugby sevens' spectacular Olympic Games debut at Deodoro Stadium.
Great Britain and Fiji faced each other in the men's final, while Australia claimed the women's title.
Rugby union is already confirmed for the Tokyo 2020 Games, while a decision on whether it remains beyond then is expected to be made by the International Olympic Committee's general assembly next year.
"It has just been such a fantastic six days," former England captain Beaumont told reporters in Deodoro.
"In rugby, we tend to think that we know it all, and you come to events that are far bigger than anything we would normally stage, and to be a part of it has just been fantastic.
"Also, for us to show the Olympic family what we can do with our sport, and in a market that wouldn't be a traditional rugby market.
"We've had an opportunity, and we thank the IOC for that.
"We've got Tokyo in four years' time, the year after the Rugby World Cup in Japan, so I can only see rugby expanding in both forms of the game.
"It has hopefully been a catalyst in South America, and when we go to Tokyo, it will enable us to expand the game more and more in Asia.
"There is nobody in World Rugby that is conceited enough to think we've got a divine right to be here, but hopefully we have showcased our sport on the world stage.
"If you think of the men's semi-finals today, there were countries from Asia, Europe, Oceania and Africa. If my geography is any good, that's not bad for a global game."
Looking beyond Rio, Beaumont added: "We will be trying like mad to retain our status (beyond Tokyo 2020).
"All the people I have spoken to have been nothing but encouraging about our sport.
"In the wash-up, there will be an assessment of how rugby performed, and there will be certain criteria around spectators, the game, the product, broadcast figures, and then the next meeting of the general assembly is in Lima, and that is when the decision will be made on whether we remain and become a core sport."
Attendance figures were also encouraging at the 15,000 capacity stadium, with a superb atmosphere accompanying the six days of action
World Rugby chief executive Brett Gosper said: "I think we got a 50 per cent fill on the first day, then straight up to 75 per cent and sat between 75-80 per cent the rest of the time.
"It sat at about 12,000 for the women's final, which is a record for the women's game."