WASHINGTON—GOP Sen. Rob Portman of Ohio is proposing legislation that would make it harder for the White House to impose the sort of duties that have hit metals imports, aiming to move beyond stalled congressional efforts to respond to the Trump administration’s national-security tariffs.

The measure, which faces longer odds in the House than in the Senate, could be most meaningful to foreign auto makers, who have been in President Trump’s crosshairs despite a recent moderation in tensions between the U.S. and European car...