WASHINGTON — The Supreme Court agreed Tuesday to hear a major challenge to the limits set by the Obama administration on emissions of mercury and other toxic pollutants from coal-fired power plants.

It is the latest effort by industry groups to roll back regulations that would reduce emissions like mercury, soot, sulfur, smog and carbon dioxide. The case also threatens to undermine one of the administration’s most significant victories and chip away at President Obama’s legacy.

John Walke, a lawyer with the Natural Resources Defense Council, called the regulation of mercury emissions that are at issue in the new case “the greatest clean air achievement of the Obama administration’s first term.”

The industry groups say the Environmental Protection Agency is overstepping its authority under the Clean Air Act by issuing the series of regulations. Republicans have attacked the rules as a “war on coal” and an example of what they say is the executive branch’s overreach.