Workers at two of the biggest U.S. steelmakers are demanding higher compensation as tariffs on foreign metal push prices and profits to their highest point in years in a buoyant economy.

Leaders for some 30,000 members of the United Steelworkers union say United States Steel Corp. and ArcelorMittal SA aren’t passing those benefits to their workers, who have gone without raises in recent years even as wages have started to climb more broadly.

President...