The EU is also maintaining a threat of counter-measures that would target US imports ranging from maize to motorcycles, and may publish its list next week to allow industry and other interested parties to give their input.
Trump suggested there would be good news just around the corner for a renegotiated NAFTA - a trade deal he has consistently dissed as bad for America.
The seventh round of NAFTA talks between the three involved nations concluded in Mexico Monday.
Both Mexico and Canada are among the main suppliers of steel to the US.
Though economists, fact-checkers and even members of Trump's own party have called the president's global trade analysis into question, inventor and Tesla chief executive Elon Musk appears to agree (in part) with Trump.
The fight over tariffs comes amid intense turmoil in the West Wing, which has seen waves of departures and negative news stories that have left Trump increasingly isolated in the Oval Office, according to two senior officials speaking on the condition of anonymity to discuss internal thinking. "That would be a case-by-case and country-by-country basis".
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Thursday's announcement from the White House that it would slap levies on imports of the key metals was met with anger from major trading partners like China, Japan and the EU.
Rep. Steve Pearce, a Republican also running for governor, said he'd try to ensure the tariffs don't hurt the state. Baoshan Iron & Steel was down 3.5 percent by 0014 GMT, while Hesteel and Beijing Shougang were down more than 1 percent. This despite fierce protests from trading partners and even collective concern from members of the Republican party who claim the measures would weaken the competitiveness of USA industries.
Arizona Sen. Jeff Flake, a Republican, said he plans to introduce legislation next week to nullify the tariffs though he has acknowledged that finding the votes to stop the president's actions could be hard.
Louisiana economists have warned that such tariffs, while meant to bring jobs back to disadvantaged US producers of aluminum and steel, would threaten the viability of industrial projects throughout the state by raising construction costs.
"That's not fair", Trump said.
"We must have a meaningful conversation about mental health issues and other possible cultural and societal contributors to violent behavior, such as violence in video games", she wrote. "Under the direction of the president, the USTR is responsible for negotiations with countries that seek an alternative means to the steel and aluminium tariffs", the White House said.