WASHINGTON, June 20 (Reuters) - The U.S. Supreme Court on Monday rejected a global warming lawsuit against five big power companies, its most important environmental ruling since 2007 and a victory for the utilities and the Obama administration.

The justices unanimously overturned a ruling by the Second Circuit U.S. Court of Appeals that the lawsuit now involving six states can proceed in an effort to force the coal-burning plants to cut emissions of gases that contribute to climate change.

In a defeat for environmentalists, the Supreme Court agreed with the companies that regulating greenhouse gases should be left to the U.S. Environmental Protection Agency (EPA) under the clean air laws.

The ruling stemmed from a 2004 lawsuit claiming the five electric utilities have created a public nuisance by contributing to climate change. The lawsuit wanted a federal judge to order them to cut their carbon dioxide emissions.

Lawyers for the power companies, including an Obama administration attorney representing the government-owned Tennessee Valley Authority (TVA), said the scope of the lawsuit was unprecedented, involving national and international issues outside the power of federal judges.

The utilities -- American Electric Power Co Inc, Southern, Xcel Energy Inc and Duke Energy Corp, along with TVA -- account for about 10 percent of U.S. carbon dioxide emissions.

The states of California, Connecticut, Iowa, New York, Rhode Island and Vermont said their citizens have been harmed by global warming and wanted their lawsuit to proceed to trial.

"The Clean Air Act and the Environmental Protection Agency action the Act authorizes, we hold, displace the claims the plaintiffs seek to pursue," Justice Ruth Bader Ginsburg said for the court.

The ruling involved the most important climate change case to reach the Supreme Court since its landmark 2007 ruling that authorized the EPA to regulate greenhouse emissions.

Although the EPA has found that greenhouse pollution poses a health hazard, it has yet to impose regulations on the power plants in the face of opposition from Republicans in Congress.

EPA SETTING RULES LIMITING EMISSIONS

Ginsburg said the EPA is currently engaged in making rules to decide whether it should set limits on emissions from domestic power plants.

"The critical point is that Congress has vested decision-making authority in the EPA," she said in summarizing the ruling from the bench.

If the plaintiffs are dissatisfied with the EPA's decision, they then can seek court review under procedures under the Clean Air Act, Ginsburg said.

Coal-fired power plants emit about twice as much carbon dioxide -- which warms the Earth by trapping solar heat in the atmosphere -- as natural gas-fired plants. Nuclear power plants emit virtually no greenhouse gases.

Peter Keisler, who argued for the power companies, said he was pleased the decision held that states and private parties should look to Congress, not the courts, to set policies on climate change and greenhouse gas regulation.

American Electric Power spokesman Pat Hemlepp said power companies that emit greenhouse gases "can continue to operate in accordance with environmental regulations without worrying about the threat of incurring substantial costs defending against climate change litigation."

David Doniger, policy director of the Climate Center at the Natural Resources Defense Council environmental group, said, "Today's ruling reaffirms the Environmental Protection Agency's duty under the nation's 40-year-old Clean Air Act to safeguard public health and welfare from dangerous carbon pollution. Now the EPA must act without delay."

The Supreme Court case is American Electric Power et al v. Connecticut et al, No. 10-174.

For American Electric Power, Inc. et al: Peter Keisler of Sidley Austin.

For Connecticut, et al: Barbara Underwood of the New York Office of the Attorney General.

For the Open Space Institute Inc et al: Matthew Pawa of the Law Offices of Matthew F. Pawa.

For the Tennessee Valley Authority: Solicitor General Donald Verrilli Jr. and Acting Solicitor General Neal Katyal of the Justice Department.

(Reporting by James Vicini)