WASHINGTON — In a setback for environmentalists, the Supreme Court justices signaled they will throw out a huge global warming lawsuit brought by California and five other states that seeks limits on carbon pollution from coal-fired power plants in the South and Midwest.

Encouraged by the Obama administration’s top courtroom lawyer, the justices said the problem of regulating greenhouses gas should be left to the Environmental Protection Agency. It is too complex and unwieldy to be handled by a single federal judge acting on a “public nuisance” lawsuit, some of them said.

A defeat for the lawsuit would put more pressure on the administration and the EPA to enforce limits on carbon pollution in the face of strong opposition from congressional Republicans, environmental advocates said.

“The stakes will be very high. The question is whether they can deliver,” said David Doniger, a climate change expert for the Natural Resources Defense Council.

The issue debated before the high court Tuesday was not whether greenhouse gases are causing global climate change, but who should regulate these gases. The decision involves politics, economics and science, the lawyers said.

“It’s a question of trade-offs,” said Peter Keisler, a lawyer representing the power producers. “There is no legal principle here to guide the decision” if it were made by a judge.

Keisler, a former Bush administration official, was joined by acting U.S. Solicitor General Neal Katyal in urging the justices to throw out the lawsuit against the power plants as too sprawling.

“In the 222 years that this court has been sitting, it has never heard a case with so many potential perpetrators and so many potential victims,” Katyal began. Everyone on the planet is an emitter of carbon dioxide, he said, and everyone is a potential victim of global warming. Judges and courts are not suited to handling “global” problems through a lawsuit, he said.

In their comments and questions, it became clear that the justices — liberals and conservatives alike — were also dubious of allowing a single judge to decide on the regulation of greenhouse gases.

This “sounds to me a lot like what the EPA does,” Justice Ruth Bader Ginsburg told a New York state lawyer who was defending the lawsuit. A judge cannot be “a super EPA” who sets and enforce detailed regulations, she said.

Four years ago, the justices cleared the way for the EPA to regulate greenhouse gases under the Clean Air Act. Since then, the government has adopted stricter standards for new motor vehicles, which take effect next year. But regulation of power plants has stalled. The agency says it will propose new rules in July.

All the while, however, the states have pressed ahead with their “nuisance” suit against the five large power producers. It began in 2004 during the time when the Bush administration insisted it had no authority to tackle global warming.

Lawyers for California, Connecticut, New York, Rhode Island, Vermont, Iowa and New York City sued the power plants that were responsible for 10 percent of the nation’s carbon emissions. They said these gases are causing the planet to heat up, posing a threat to the coastal communities in the East and West and to crops in the heartland. It asked for a judge to impose limits on these emissions.

Four more states — Illinois, Maryland, Massachusetts and North Carolina — endorsed the suit when it reached the high court. But 23 other states, led by Indiana, said the suit poses a “political question” that should not be resolved by a judge.

The first judge who heard the suit dismissed it. But to the surprise of the electric power industry, the U.S. court of appeals in New York revived it.

Prior to the passage of the Clean Air Act and Clean Water Act in the early 1970s, it was common for anti-pollution suits to be brought as “public nuisance” claims. For example, a downstream state could sue another upstream for putting pollutants in a river.

Though such suits are rare today, Barbara Underwood, the New York state lawyer, said the interstate global warming suit should go forward because the EPA has not dealt with carbon pollution from power plants. “It could be a long time before the EPA acts,” she said.