Most pressing is the crisis in Venezuela, where the USA and Brazil - and dozens of other countries - have recognised opposition leader Juan Guaido as interim president with the goal of forcing President Nicolas Maduro from power.
At Tuesday's news conference, the two presidents repeatedly rejected socialism, celebrating their joint efforts to oust Venezuela's left-wing leader, Nicolas Maduro.
After his arrival, Bolsonaro was scheduled to dine at the residence of Brazilian Ambassador Sergio Amaral with "opinion makers" including, according to press reports, former Trump adviser and far-right activist Steve Bannon and US-based Brazilian writer Olavo de Carvalho, considered Bolsonaro's ideological guru.
Supporting Brazil for an association with North Atlantic Treaty Organisation would be a considerable step further, one that Trump recognized would mean he would "have to talk to a lot of people". "There's zero hostility with me".
It is Bolsonaro's first trip overseas for a bilateral meeting since taking office on January 1, after he attended the Davos summit in Switzerland in January.
Bolsonaro pledged during his campaign to build closer ties with the U.S. and has often expressed admiration for Trump.
Trump praised Bolsonaro for his comments about fake news, saying: "You look at the networks, you look at the news, you look at the newscasts - I call it fake news".
The conviviality was cemented when the men exchanged soccer jerseys from their country's respective national teams.
Bolsonaro has sought to underscore his pro-America stance throughout his visit. In addition, Brazil will allow the importation of American pork.
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China long ago surpassed the United States as Brazil's biggest trading partner and Bolsonaro's economy minister on Monday urged the United States to open its market more to Brazil if it wanted to change the status quo.
Bolsonaro, who was accompanied on his trip to the United States by his son, lawmaker Eduardo Bolsonaro, visited Central Intelligence Agency headquarters in Langley, Virginia, on Monday and addressed the U.S. Chamber of Commerce.
The two were slated to work toward creating a "north-south axis" between the U.S. and Brazil on economic issues as the two largest economies in the western hemisphere, the official said.
"We have to sort Venezuela out", Bolsonaro said.
Mr Bolsonaro succeeded a leftist who at times had a frosty relationship with the US.
In 2013, leaks from Edward Snowden revealed that the National Security Agency had wiretapped conversations of then-President Dilma Rousseff, leading to a years of frosty relations between the US and Brazil.
The official said the president took note of Bolsonaro's Trump-like rhetoric and social media presence, and called Bolsonaro to congratulate him within hours of his election.
The remarks were aired after the two countries signed several bilateral agreements, including one that allows the United States to use Brazil's Alcantara Aerospace Launch Base for its satellites, and Brazil announced an end to visa requirements for USA tourists who visit the country. The Bolsonaro administration is seeking to reduce public-sector spending and privatize state enterprises to reduce debt and grow its economy.
Venezuela is expected to be a subject of discussion.
They struck initial agreements on agricultural trade, with better access for American wheat and pork exports to Brazil and the possibility of restarting sales of Brazilian fresh beef to the United States.