WASHINGTON — The Environmental Protection Agency declined on Friday to relax its requirement on the use of corn ethanol in gasoline, rejecting a request from several states related to a steep decline in the nation’s corn production.

A summer drought that withered crops led to a spike in prices, hurting the livestock industry and others that depend on corn for food. Estimates indicate that as much as half of the nation’s crop will be used to produce ethanol this year to meet the federal renewable energy standard for transportation fuel.

“We recognize that this year’s drought has created hardship in some sectors of the economy, particularly for livestock producers,” Gina McCarthy, an E.P.A. assistant administrator, said in a statement. “But our extensive analysis makes clear that Congressional requirements for a waiver have not been met.”

To approve a change in the standard, the agency would have to conclude that the fuel rule would “severely harm” the economy. The E.P.A. said it had analyzed 500 potential market variations and that most of them showed no impact from the use of corn for ethanol; those that did showed an average impact of 7 cents a bushel, less than 1 percent of the price, it said.