The NAFTA is a deal signed by Canada, Mexico, and the US, creating a trilateral trade bloc in North America.
Australia has a trade and investment deficit with the United States, which is understood to have played a considerable role in alleviating Mr Trump's sense of grievance.
Shortly after Trump's tweet, Australian Prime Minister Malcolm Turnbull said on Twitter the relationship between the two allies was fair and reciprocal.
In a speech in the United States on Sunday, Mr Trump lashed out at the European Union, saying they erected "horrific" trade barriers based on environmental and other regulations.
The big worry is that United States trading partners will retaliate. "Working very quickly on a security agreement so we don't have to impose steel or aluminum tariffs on our ally, the great nation of Australia!"
French economy minister Bruno Le Maire told reporters: "We are anxious (about) the possibility of having a trade war between the United States and the European Union because we believe that there will be only losers".
No wonder the announcement spurred the resignation of White House chief economic adviser Gary Cohn, one of many who had unsuccessfully warned against the plan.
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While that kind of talk makes agriculture very nervous, Mr. Trump said he is optimistic there will be a NAFTA deal, "I have a feeling we are going to make a deal on NAFTA".
Mr. Trump threatened to tax European-made cars if they retaliated against the aluminum and steel tariffs with their own taxes on USA imports like Harley Davidson motorcycles, bourbon and blue jeans.
"That being said, any benefits attributable to tariffs are likely to be outweighed by costs".
In signing the order last week, the President made it clear that if Canada and Mexico made concessions during the NFTA negotiations, they would be exempted from the tariffs.
Asked about Trump's tweet, the European Union in a statement said that "no further meetings as such are planned at the moment". Companies that export their metal products to Mexico and Canada were particularly fearful of tariff retaliation by those countries if they are not exempted.
The European Union said it could respond with their own tariffs for American products which would include oranges, bourbon, denim, cranberries, peanut butter and motorcycles. "If you're thinking about trying to get your key partners to actually cooperate with you on the underlying issue ... it's going to be much more hard to get them to do so if at the same time you're hitting them with tariffs". "It has a negative impact on the NAFTA talks". What the USA is using is a security excuse. But it will hurt firms which export pipes and tubes besides stainless steel, which account for 34 per cent of the steel exports to the US.