Leading Republicans turned up the pressure on Mr Trump, with House of Representatives Speaker Paul Ryan leading the charge. "Tariffs on Steel and Aluminum will only come off if new & fair NAFTA agreement is signed", Trump tweeted.
Leaders of the House Ways & Means Committee have drafted a letter to Trump expressing concerns about "the prospect of broad, global tariffs on aluminum and steel imports", according to Lauren Aronson, spokeswoman for the committee Chairman Kevin Brady.
In a rare public split, House Speaker Ryan's office said they were "urging the White House to not advance with his plan".
Efforts by Mr Trump and U.S. trade negotiators to link the Nafta trade pact talks to the duties received short shrift from Ottawa and Mexico City.
President Donald Trump should take "surgical" action against countries that dump steel and aluminum in United States markets rather than follow through on a risky threat of global tariffs, Congress's top Republican said Tuesday.
The letter doesn't mention any countries as potential targets.
President Trump, meanwhile, has continued defending his plan. Economists say that could lead to inflation.
European Commission chief Jean-Claude Juncker has vowed to fight back against US President Donald Trump's threat of a 25% tariff on steel and 10% on aluminum imports.More news: Democratic Party Set To Show Its Force In Nation's First 2018 Primary
The President also tweeted about the issue Sunday evening and Monday morning.
Addressing WTO members today, he argued: "We can not ignore this risk and I urge all parties to consider and reflect on this situation very carefully". The latest round of a almost year-long renegotiation effort is concluding this week in Mexico City.
He wrote on Twitter later that if the European Union increases tariffs on United States goods "we will simply apply a Tax on their Cars which freely pour into the U.S. They make it impossible for our cars (and more) to sell there".
White House trade adviser Peter Navarro told "Fox and Friends" on Monday that there are "virtually no costs here".
"Firm line in the sand", he says.
Even as the din is getting louder, every country takes solace in the fact that Trump is notorious for backing out of his controversial decisions.
If the US can impose these tariffs on steel and aluminum on the basis of "national security", someone else is sure to try for tariffs on food, or clothing, or various other products on the same basis.
The tit-for-tat between the United States and EU has already had an impact on European auto makers, whose share prices dropped on Monday following a threat by Trump to tax their vehicles.