A federal appeals court on Tuesday ordered the Environmental Protection Agency to relax some limits it set on smokestack emissions that cross state lines and taint downwind areas with air pollution from power plants.

At the same time, the court upheld the EPA's right to impose the clean-air standards, rejecting an argument by states and industry groups that the rule was overly burdensome.

The ruling by the U.S. Court of Appeals for the District of Columbia Circuit orders the EPA to redo sulfur-dioxide and nitrogen-oxide standards for 13 states, mostly in the South and Midwest, that contribute to soot and smog along the East Coast.

Texas and South Carolina would see limits for both forms of pollution adjusted, while new limits for either sulfur dioxide or nitrogen oxide would be set in 11 other states: Alabama, Georgia, Florida, Maryland, New Jersey, New York, North Carolina, Ohio, Pennsylvania, Virginia and West Virginia.

The ruling follows a Supreme Court decision last year upholding the so-called Cross-State Air Pollution Rule, which blocks states from adding to air pollution in other states.

The April 2014 ruling was an important victory for the Obama administration and capped a decades-long effort by the EPA to ensure that states are good neighbors and don't contribute to pollution problems elsewhere.

Industry groups and many of the affected states have cast the rule as an attempt to step on states' rights and shut down aging coal-fired power plants as part of what many Republicans call a "war on coal" by the Obama administration.

An EPA spokeswoman said the agency was pleased that the court decision keeps the Cross-State Air Pollution Rule in place "so that it continues to achieve important public health protections."

The EPA remains committed to working with states and power companies as it moves to implement the rule, spokeswoman Melissa Harrison said. "We are reviewing the decision and will determine any appropriate further course of action once our review is complete," she said.

The Supreme Court said the EPA, under the Clean Air Act, can implement federal plans in states that do not adequately control downwind pollution. But the court also ruled that the EPA can consider the cost of pollution controls and does not have to require states to reduce pollution by the precise amount they send to downwind states.

The appeals court, in its ruling, said the EPA's rule imposed overly strict limits on the 13 upwind states. As a practical matter, the limits would result in downwind states "overachieving" air quality standards for sulfur dioxide and nitrogen oxide, the court said.

Frank O'Donnell, president of Clean Air Watch, an environmental advocacy group, scoffed at the idea that the EPA rule was overly strict.

"The reality is we need more pollution control of power plants, not less," he said, noting that the pollution standards used by the EPA were developed in the 1990s.

"The targets involved in this case are so outmoded that they are almost irrelevant," O'Donnell said.

"We know in reality that these power plants are going to have to clean up even more to meet modern standards," O'Donnell added, referring to new EPA rules on soot and smog expected in the next few months.

The EPA says the Cross-State Pollution Rule would cost power-plant operators about $800 million a year. Those investments would be far outweighed by the hundreds of billions of dollars in health-care savings from cleaner air, the agency said. The rule could prevent more than 30,000 premature deaths and hundreds of thousands of illnesses each year, the EPA said.