"We are here to put at ease the minds of all residents and tourists coming to the games," Ricardo Barros said at a news conference Friday.
He cited a study by Cambridge University that concluded there was only a very low chance that any of the expected 500,000 foreign tourists would get the virus.
The Zika virus was detected in Brazil last year and has since caused a huge surge in birth defects.
Last month, 150 scientists and doctors posted an open letter arguing that the 2016 Summer Games should be postponed or moved.
When asked Friday whether there is a risk that the World Health Organization could end up recommending that the Games be postponed during its meeting next week, Barros said, "We don't consider the hypotheses of postponing the games. There is no scientific basis that recommends that kind of decision."
A handful of athletes have expressed concern over the virus. Some have even pulled out of the competition.
British long jumper Greg Rutherford announced that he
has frozen a sperm sample, also over Zika concern.
But on Friday, Barros noted that the Summer Games will be held in Brazil's winter, when the Aedes Aegypti mosquito that transmits the disease tends to die off.
He said the latest stats show that the number of Zika cases has fallen 87% in Brazil since the peak in February and suggested that in August, tourists would face a bigger threat in Caribbean islands, where the virus is also present and it will be the hot, muggy summer season.
Since the virus was first detected in the country, the Brazilian Health Ministry has confirmed 1,489 cases of Zika-related microcephaly, a rare birth defect in which babies are born with abnormally small heads and other neurological problems. It is still investigating more than 3,000 suspected cases.
The WHO advises
that pregnant women should avoid areas with Zika and says people returning from areas with Zika should adopt safe sex practices for at least eight weeks upon return.
Though there appears to be disagreement within medicine on what to do, the WHO has downplayed the risks of the Rio Olympics sparking a global epidemic.
"Cancelling or changing the location of the 2016 Olympics will not significantly alter the international spread of Zika virus," the WHO said in a statement. "Brazil is one of almost 60 countries and territories which to-date report continuing transmission of Zika by mosquitoes. People continue to travel between these countries and territories for a variety of reasons. The best way to reduce risk of disease is to follow public health travel advice."