Inside the White House, there still appeared to be confusion about the timing and extent of the planned tariffs, which would hit allies like Canada and Mexico hard.
Efforts by Trump and US trade negotiators to link the NAFTA trade pact talks to the duties received short shrift from Ottawa and Mexico City.
Leading Republicans turned up the pressure on Trump, with House of Representatives Speaker Paul Ryan leading the charge. Ryan's home state of Wisconsin would be hit by proposed European counter-measures on Harley-Davidson Inc motorbikes.
Representative Kevin Brady, another top House Republican, called on Trump not to hit US' closest allies.
Business leaders are pressing for a meeting with Trump to brief him on the negative repercussions of the tariffs on companies that use steel and aluminum, a source familiar with the matter said.
A meeting had not yet been set up, the source said. The White House had no comment.
The planned tariffs have roiled world stock markets as investors worried about the prospect of an escalating trade war that would derail global economic growth. Stocks across the globe rose on Monday, however, after four days in decline as investors saw the tariff threats as a US negotiating tactic and not a done deal and as pressure grew on Trump to back off.
"We're not backing down," Trump said during a White House meeting with Israeli Prime Minister Benjamin Netanyahu. "I don't think you're going to have a trade war," he added, without elaborating.
Canadian Prime Minister Justin Trudeau called Trump on Monday to tell him the tariffs would be an impediment to talks on updating NAFTA, a Canadian government official said.
Canada is the single largest supplier of steel and aluminum to the US. In the call, Trudeau "forcefully defended" Canadian workers and industries, said the official, describing the conversation as constructive.
Earlier comments from Trump had stoked talk of a global trade war as he described them as easy to win and issued a threat to German carmakers. One of those, BMW, runs a plant in the US that is the largest single autos exporter in the country and has created thousands of jobs.
Most responses to Trump's proposed tariffs have been targeted. The EU said it would hit Harleys, bourbon and jeans, iconic American products.
Trump was expected to finalize the planned tariffs later in the week, although some observers familiar with the process said it could occur next week.