President Donald Trump's effort to roll back Obama-era climate change policies will not do much to improve demand for coal at America's power plants, Royal Dutch Shell Chairman Chad Holliday said Thursday.

Coal's use in U.S. power plants has been falling for years in the face of stiff competition from natural gas. Former President Barack Obama's initiatives to rein in the impacts of climate change have hastened the retirement of old, inefficient coal-fired plants and the switch to cleaner-burning natural gas.

On Tuesday, the Trump administration lifted Obama's moratorium on new coal mining leases on federal land and set in motion the repeal of his landmark Clean Power Plan, a regulation aimed at reducing carbon emissions from smokestacks, particularly at coal-fired facilities.

But Holliday said the fundamental economics of natural gas are "pretty strong" compared with those of coal.

"Where coal can compete, coal should compete, but I think it's going to be a challenging role for them," he told CNBC's "Squawk on the Street" on Thursday.