White House press secretary Sarah Sanders said "potential carve-outs for Mexico and Canada" may be signed.
Action that does not include exemptions risks retaliatory tariffs on USA exports - not least by Canada and Europe - and complicates already tough talks on the North American Free Trade Agreement (NAFTA).
Now, Navarro and the protectionist trade policies he espouses are taking center stage as President Donald Trump prepares to make official the sweeping steel and aluminum tariffs that he and Navarro have long championed.
The European Union has warned it could retaliate on U.S. imports, including products such as motorbikes, bourbon and jeans.
The greenback had weakened sharply following the resignation on Tuesday of Gary Cohn, the top economic advisor to the White House who was seen as seen as a bulwark against protectionism in President Donald Trump's administration.
Jason Ware, chief investment officer at Albion Financial in Utah, said that with Trump keeping a close eye on stock indexes, selling sparked by tariff and trade war talks could change the president's mind.
The official said that Mr Cohn had told the president in February that he felt underused and that he should have a larger role in the White House - and if that wasn't possible, he would consider leaving.
"China has been asked to develop a plan for the year of a One Billion Dollar reduction in their massive Trade Deficit with the United States", he tweeted. "He is a rare talent, and I thank him for his dedicated service to the American people", Trump said in a statement.
And this week the administration has been hinting at a possible middle-of-the road approach: temporary relief for Canada and Mexico, with the threat of tariffs as a US negotiating weapon at the NAFTA bargaining table.
"Along with tariffs, weakening your own currency becomes a weapon in a trade war", he said.
The EU has grown increasingly exasperated with Trump's "America First" agenda, viewing it as a threat to the multilateral trade order that the USA played a leading role in building after the Second World War.
Bishop said she will be putting Australia's case to Rex Tillerson, the US' current Secretary of State, in a meeting later today.
Sen. Susan Collins, a Republican from ME, said she was sorry that "the President will no longer have the benefit of (Cohn's) advice".
After days of drama and a last-minute diplomatic scramble, the White House is now hinting that the impending tariff announcement might have some particular exceptions based on national-security considerations for the USA neighbours.
The threat of retaliation over the tariffs, which the International Monetary Fund has warned could eventually damage growth, is already rising. This will be Trump's first visit to the Golden State.
Japan has requested that the United States exempt it from the planned measure, saying Japanese steel and aluminum exports do not pose a threat to USA national security. Cohn, a registered Democrat, had become an invaluable asset for congressional Republicans, helping usher through the party's massive tax package a year ago and serving as an economic liaison to a White House that some on Capitol hill have found to be chaotic, divided and hard to predict at times. The Canadian dollar was down 0.21 percent to 1.29 per US dollar.
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