WASHINGTON — The Supreme Court on Tuesday agreed to hear a major case challenging Environmental Protection Agency regulations of greenhouse gas emissions from stationary sources like power plants. The justices declined to hear a variety of related attacks on the agency’s authority to address climate change.

The case is a sequel to Massachusetts v. Environmental Protection Agency, a 2007 decision that required the agency to regulate emissions of greenhouse gases from new motor vehicles if it found they endangered public health or welfare. Two years later, the agency made such a finding, saying that “elevated concentrations of greenhouse gases in the atmosphere” pose a danger to “current and future generations.” It set limits on emissions both from new vehicles and from stationary sources like power plants.

States and industry groups challenged the regulations on several grounds. They said the agency’s conclusions about the dangers posed by greenhouse gases were not supported by adequate evidence, that the so-called tailpipe regulations were flawed and that the agency was not authorized to regulate emissions from stationary sources.

A three-judge panel of the United States Court of Appeals for the District of Columbia Circuit last year unanimously rejected the challenges, some on the merits and some on the ground that the parties before the court lacked standing to pursue them.