"We (the U.S.) are looking at it strongly, we are very inclined to do that, the relationship that we have right now with Brazil has never been better, I think there was a lot of hostility with other presidents, there is zero hostility with me", Trump said as he sat alongside President Jair Bolsonaro.
It was the Brazilian president's first trip overseas for a bilateral meeting since taking office on January 1.
A senior member of Bolsonaro's economic team said last week Brazil did not expect the US government to announce support for its bid to join the OECD during Bolsonaro's visit.
Outside the White House Sunday afternoon, dozens of demonstrators gathered to protest the visit - holding signs including one that accused Bolsonaro of being a "murderer" over apparent links to suspects in the murder of rights activist Marielle Franco.
Brazil also hopes to see itself elevated to "major non-NATO ally" status by the President Trump administration, a major step that could help it purchase military equipment. But proposing Brazil for North Atlantic Treaty Organisation membership would take that a step further.
If the leaders of the Americas' two most populous democracies form a strong bond, they could work in concert on a range of regional issues.
The tough-talking Bolsonaro has long expressed his admiration for Trump. Some used the hashtag #BolsonaroandTrump to herald the meeting of the USA president with the man the foreign press has dubbed "Trump of the Tropics".
The older Bolsonaro announced on Saturday that one key result of his current trip would be the signing of an agreement under which the United States might gain access to a satellite-launching base in Brazil near the equator.
A senior administration official said Brazil plays an important role as an "interlocutor" between the USA and Venezuela.
The far-right Bolsonaro was elected previous year and is an admirer of President Donald Trump.
Brazil shares a border with Venezuela and, like the United States, has joined with dozens of other world leaders in pressuring socialist Nicholas Maduro to turn over power to opposition leader Juan Guaido.
The 63-year-old former paratrooper is vehemently opposed to leftist currents, at home and overseas, and he shares Trump's hostility to the "dictator" Maduro, who took over after the death of socialist leader Hugo Chavez in 2013.
Ahead of Tuesday's Oval Office meeting, Bolsonaro waived a visa requirement for US visitors to Brazil and later in a Fox News interview on Monday night threw his weight behind Trump's immigration agenda, which includes a wall on the Mexican border.
But Bolsonaro, 63, has ruled out military action in favor of a policy of increasing the economic and diplomatic pressure on Maduro. 'It's the beginning of a partnership focused on liberty and prosperity, something that all of us Brazilians have long wished for'.
The MNNA designation would ease the transfer of defence technology at a time when Brazil's aerospace industry has forged new ties with the United States, including a planned tie-up between Boeing Co and Brazilian plane maker Embraer SA on both defence and commercial aircraft.