"The situation does not compromise the Olympics," Rousseff said. "We are confident that until the Olympics begin we will have considerable success in exterminating" the Aedes aegypti mosquito that transmits the virus.
Rio de Janeiro will host the Summer Olympics August 5 to 21, drawing athletes and spectators from around the world.
Rousseff spoke to reporters after visiting two houses in a suburb of Rio de Janeiro as part of a national awareness campaign to stop the virus from spreading.
While it causes only mild symptoms in most people, Zika has been linked to a rapid rise in the number of children born with microcephaly -- abnormally small heads and brains -- to mothers infected during pregnancy.
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Warning that pregnant women were especially at risk, Rousseff urged all Brazilians to come together.
"The war depends on us," said Rousseff, accompanied by officials, health workers and a swarm of journalists.
"The government is taking the lead but that alone won't win the war," she added. "We need to get everyone involved."
Troops will visit three million homes to make people aware that many mosquito breeding areas are found in homes.
For example, mosquito larvae can live in standing water in flower pots.
There is currently no cure or vaccine for Zika.