WASHINGTON — 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 oxides would be set in 11 other states: Alabama, Florida, Georgia, Maryland, New Jersey, New York, North Carolina, Ohio, Pennsylvania, Virginia and West Virginia.