Rousseff presided over the flame ceremony in Brasilia, even though she faces impeachment and is unlikely to be in office when South America's first Olympics open in less than three months.
"Brazil is ready to host the most successful Olympics in history," Rousseff said in a speech to off the torch relay, which will reach 329 Brazilian cities and end on August 5 at the opening ceremony in Rio's Maracana stadium.
However, security experts have been expecting protests during the relay, and today a few hundred protesters gathered on a relay route controlled with a heavy police presence.
Rousseff is expected to be suspended from office next week as the country's senate hears an impeachment case against her, which means Vice President Michel Temer is likely to be president during the games.
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Rousseff spoke for 20 minutes, promising Rio is ready with completed venues and top security.
"Brazil is completely ready to offer protection to the athletes, the technical staffs, heads of delegations, tourists, and journalists to all our visitors," she said.
Rousseff said the country was working with international security agencies "who have experience with terrorism."
She also touched on the political and economic turmoil rocking South America's largest country.
"We know political problems exist in our country today," she said. "We know there is political instability. Brazil will be capable in a difficult period, a very difficult, critical period in the history of our democracy of dealing with the problems. ... It's important to fight, and we know how to fight."
The Olympic flame arrived in a lantern on a flight from Switzerland and was taken to the Planalto presidential palace.