WASHINGTON — President Trump, responding to companies’ struggles with a shortage of skilled workers that has left more than six million jobs unfilled nationwide, signed an executive order Thursday geared at better aligning government training programs with the demands of industry.

The order creates a Council for the American Worker, led by the secretaries of commerce and labor, that will focus on consolidating existing federal programs and funding new job training initiatives, with a special concentration on expanding apprenticeship programs and retraining older workers without college degrees.

As part of the effort, companies and trade unions have committed to funding nearly four million slots for apprenticeships, retraining and continuing education programs over the next five years.

Job training has emerged as one of the few coordinated policy initiatives generated in the West Wing with broad appeal across income and party lines. In part, that is because many labor and corporate leaders are struggling to expand their work force, and several top White House officials, including Kevin Hassett, the chairman of Mr. Trump’s Council of Economic Advisers, have made the issue a top priority.