“What they’ve done to our dairy farm workers is a disgrace,” Mr. Trump said as he ordered a sweeping investigation into whether steel imports are harming America’s national security. “We can’t let Canada or anybody else take advantage and do what they did to our workers and to our farmers.”

Mr. Trump admitted he was going off script because the steel order is aimed at more familiar trade boogeymen like China and Japan. But his outburst in the Oval Office toward a friendly neighbor punctuated a week when tough talk on trade took center stage in a White House deeply divided over how aggressively to erect the trade barriers that Mr. Trump promised during his campaign.

From Mr. Trump’s “buy American, hire American” rallying cry in Wisconsin this week to Vice President Mike Pence’s warnings to Japan and South Korea about the need to rewrite trade deals, the Trump administration is moving against free trade on multiple fronts. A senior White House official said there would be two trade-related events a week for the next few weeks.

“He’s manically focused on these trade issues,” said Stephen K. Bannon, the president’s chief strategist.