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In a TV speech, Bolsonaro said the moment "calls for union."
"Even though things can get worse, there is no reason for panic. The best protection is to follow the recommendations of specialists rigorously," he said.
As the virus presents a new challenge to the world, the Brazilian Health Ministry is giving assistance to local health authorities in dealing with the disease, the president said.
Earlier in the day, the health ministry updated the number of confirmed COVID-19 cases in the country to 13. Among them, 10 cases were registered in Sao Paulo Municipality, and the other three were in the states of Rio de Janeiro, Espirito Santo and Bahia, respectively.
A case in Brazil's capital city Brasilia is awaiting confirmation of a presumptive positive test result.
So far, 11 cases are linked to travel to Europe and the United States. The other two are relatives of the first patient in Brazil. The patient participated in a family reunion before showing symptoms of COVID-19 infection, and his relatives have been quarantined.
In addition to the 13 confirmed cases, there are still 768 suspected cases in Brazil.