The White House said the levies would be looked at “country by country” after a backlash from around the world.
China threatened an “appropriate and necessary response” in any trade war with the US.
Foreign Minister Wang Yi said China and the US should aim to be partners rather than rivals.
And the EU vowed to retaliate, drawing up a list of 100 US brands to target should Mr Trump start a trade war.
Canada and Mexico could be offered a 30-day exemption from Donald Trump’s planned tariffs on steel and aluminium imports according to the White House.
The 25 percent levy on steel imports and 10 percent on aluminium goods could be wiped for Canada and Mexico as the US renegotiates terms of its North American Free Trade Agreement (NAFTA).
Speaking about the tariffs, White House spokeswoman, Sarah Saunders, said: “We expect that the president will sign something by the end of the week and there are potential carve-outs for Mexico and Canada based on national security, and possibly other countries as well based on that process.
“It will be country by country, and it will be based on national security.”
Both Mexico and Canada are among the main suppliers of steel to the US.
Business officials and congressional Republicans have voiced concern about the tariff’s impact on their economy.
One of President Trump’s campaign promises was to rebuild the US steel and aluminium industries, which he claimed have suffered “disgraceful” treatment from other countries, in particular Chinese imports.
On Wednesday, President Trump tweeted: “From Bush 1 to present, our Country has lost more than 55,000 factories, 6,000,000 manufacturing jobs and accumulated Trade Deficits of more than 12 Trillion Dollars.
“Last year we had a Trade Deficit of almost 800 Billion Dollars. Bad Policies and Leadership must win again.”