"I think he could be an adequate appointment and could perfectly handle things in Washington", Xinhua news agency quoted the President as saying on Thursday.
"Eduardo is a friend of Donald Trump's children, speaks English and Spanish, and has long experience with world affairs".
On Friday, Bolsonaro said in a Facebook Live that he "is not concerned" about the criticism he was receiving over the nomination idea.
"I did an exchange, I fried hamburgers", the federal lawmaker told reporters, a day after his father said he was considering appointing him to Brazil's most important diplomatic posting, sparking accusations of nepotism.More news: Hotel attack leaves at least 10 dead in Somalia
"It is a total scandal ... a flagrant case of nepotism that can not be accepted", Folha de Sao Paulo quoted opposition representative Randolfe Rodrigues as saying. "This is a complete mess".
A 2008 Supreme Court decision prohibits Brazilian authorities from nominating close family members to official posts, but the ruling was vague and Bolsonaro's allies argue it doesn't apply in this case.
A 2017 YouTube video shows him standing in front of a Popeyes chicken counter recounting his time in the United States between 2004 and 2005.
Though he is now the chief of the Foreign Liaison Committee of the House of Representatives, he has not actually held any diplomatic position before.More news: Axe falls on judge over video leak
Eduardo, now a member of parliament, accompanied his father to a private meeting with Trump during a diplomatic visit to Washington in March. The statement caused disapproval at home.
Mr Bolsonaro was elected a year ago after a successful campaign he said had been inspired by Donald Trump.
Jair Bolsonaro's son, Eduardo, will have to resign his seat in Brazil's Congress and get senate approval if he is picked to be ambassador to the United States.
Brazil's President Jair Bolsonaro, on March 12, 2019. "Brazil is not in the top 10", Stuenkel said. "Eduardo Bolsonaro's nomination for ambassador is unacceptable".More news: Dragon Quest Builders 2: How to Make Farmer's Bedroom
The set of ambassador has been vacant since April.
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