WASHINGTON — A coalition of 29 states and citie s on Tuesday sued to block the Trump administration from easing restrictions on coal-burning power plants, setting up a case that could determine how much leverage the federal government has to fight climate change in the future.

The lawsuit is the latest salvo in a long-running battle over the future of coal and how to regulate the nation’s heavily polluting power plants, which are major producers of greenhouse gases that warm the planet. It also is the most significant test to date of the Trump administration’s efforts to eliminate or weaken former President Obama’s regulations to reduce the United States’ contribution to global warming.

It is a case that could go all the way to the Supreme Court. If justices there were to ultimately decide in favor of the Trump administration, it could weaken the ability of future presidents to regulate carbon dioxide pollution from power plants, experts said, and make it harder for the United States to tackle climate change.

“It would have a devastating effect on the ability of future administrations to regulate greenhouse gases under the Clean Air Act,” said Richard L. Revesz, a professor at New York University who specializes in environmental law, referring to a 1970 law that requires the Environmental Protection Agency to regulate hazardous air pollutants.