President Barack Obama used a campaign trip to the industrial Midwest—where he and Republican challenger Mitt Romney are battling for working-class votes—to showcase the U.S. escalation of the trade fight with China, accusing Beijing of unfairly subsidizing its auto-sector exports.

Mr. Obama announced in Ohio on Monday that the administration had lodged a new complaint against China at the World Trade Organization, the international arbiter of trade disputes. China launched its own challenge Monday of a U.S. tariff law.

“These are subsidies that directly harm working men and women on the assembly lines in Ohio and Michigan and across the Midwest.” Mr. Obama said. “It is not right. It is against the rules. And we will not let it stand.”

Mr. Romney, who recently sharpened his criticism of Mr. Obama as weak on China, described the president’s move as “too little, too late.”