WASHINGTON—President Donald Trump is expected to sign a decree this week laying out his plan to impose new tariffs on steel and aluminum, sparing both Canada and Mexico, after people on both sides of the issue made final pleas to either scuttle the measure or ensure he doesn’t back off.

At the White House on Wednesday, aides began preparations for the ceremony ushering in a turn in trade policy that could recalibrate relations between the U.S. and its allies and trading partners.