The petitions for asylum came as Bolsonaro threw his support for the attempted coup in a series of tweets.
About 25 Venezuelan troops have sought asylum in Brazil's embassy in Caracas, Brazil's government spokesperson Otavio Rêgo Barros said Wednesday, shortly after the attempted coup against President Nicolas Maduro.
In an interview with Folha de S.Paulo, Rêgo Barros reported 25 had applied so far, adding that President Jair Bolsonaro had already authorized the requests.
Foreign Minister Ernesto Araujo reiterated Brazil's support for a "democratic transition" and expressed "hopes that the Venezuelan military will be part of this process."
An apparently carefully planned attempt by Guaido to demonstrate growing military support on Tuesday quickly failed.
Senior government officials have rejected the attempted coup and called on the country's population to do the same and march towards the Miraflores presidential palace to protect the country from the far-right, U.S.-backed coup.
Thousands of citizens marched Tuesday to the palace to attend a rally led by the head of the National Consistent Assembly Diosdado Cabello.