The mining industry is threatening to sue the Labor Department if it doesn’t strike down an Obama-era workplace inspection rule.

Mining industry representatives say that the Mine Safety and Health Administration’s rule (RIN: 1219-AB87), violates the White House’s Jan. 20 executive order requiring agencies to take back rules that hadn’t been published in the Federal Register. That’s because it was published three days after the order.

The mine exam rule requires operators to complete their safety inspections before miners enter the work site before a shift starts. Previously, those exams could be conducted after miners...