Rousseff made the comments during the official opening of the 15,000-seat Olympic aquatic centre, which will host swimming and water polo during the August 5-21 Games, Xinhua reported.
"We will stage this Olympics in the same way that we staged the  World Cup, with peace and tranquility," Rousseff said.
"It is very important to guarantee to all the athletes and visitors from all over the world that the Games will be, without any doubt, an event underlined by peace, unity of people and dialogue."
Rousseff suggested the Olympics could represent that start of a recovery for Brazil's stricken economy.
"This is a special moment. It is a symbol and an example for Brazil of what is possible when good people work together. If we are capable of hosting the Olympic Games we are also capable of helping our country to grow again," she said.
Unlike the lead-up to the World Cup, Rio's Olympic preparations have mostly avoided controversy about venue delays and budget overruns. With just less than four months remaining until the opening ceremony, most sporting facilities are ready.
However, infrastructure projects like a new metro line and a light rail service linking the city centre to the port are yet to be finished. Organisers have also said they will not fulfil a pledge to reduce pollution in Guanabara Bay by 80 percent.
The total cost of staging the Olympics will reach 39.1 billion reais ($11 billion), according to the latest estimate by Brazil's Olympic Public Authority.(IANS)