The United States and China filed dueling complaints at the World Trade Organization on Monday, sharpening what has become a steady trade skirmish between the world’s two biggest economies and pushing the issue to the forefront of the presidential campaign.

As President Obama and GOP challenger Mitt Romney traded jabs over who would best manage economic relations with China, the United States alleged in a WTO complaint that the Chinese government provided its auto parts makers with hundreds of millions of dollars annually in improper export subsidies.

The political sparring in the United States comes at a time when China is confronting political challenges of its own as a new leadership prepares to take over. The country’s rapid expansion has cooled, putting the ruling Communist Party at risk of missing economic growth targets — and probably curbing any appetite for the sort of reforms demanded by Washington.

Although China has been encouraged to rely more on its domestic consumer spending for growth, exports remain central to the country’s economic strategy, and they have been hit by the economic crisis in Europe and the ebbing world recovery. The country also is mired in a territorial dispute with Japan that has disrupted factories, retailers and tourism in the face of public protests.

China’s auto parts exports have risen tenfold in the past decade, to around $70 billion annually, according to U.S. officials. The country is now the fourth largest foreign supplier to the U.S. auto industry, providing around $10 billion in parts each year.

That is far behind Mexico, where a vibrant auto industry exports around $28 billion annually to the United States under the terms of the North American Free Trade Agreement. Nonetheless, a senior U.S. official said that China’s subsidies were “flooding the world with cheap auto parts” and threatening to further disrupt a beleaguered U.S. auto parts industry.

The Chinese Embassy in Washington did not respond to requests for comment. China often responds to WTO and other trade complaints with government statements issued a day or more after actions are filed.

Obama used a campaign stop in the heavy-industry battleground of Ohio to press his case that his administration, through the auto company bailouts and other steps, was trying to boost U.S. manufacturing, and he criticized Romney for outsourcing jobs through deals at his former private equity firm.

“You can’t stand up to China when all you’ve done is send them our jobs,” the president said. “When the playing field is level, America will always win. . . . We don’t need folks who, during election time, suddenly are worrying about trade practices, but before the election are taking advantage of unfair trade practices.”

Romney characterized the latest WTO case as an election-season tactic. His campaign has begun a new television ad focusing on China’s manufacturing rise, and he has said that if elected he would deal more forcefully with issues like China valuing its currency to aid its exporters.

The WTO filing “may sound good on the stump, but is too little too late for American businesses and middle-class families,” Romney said.

The U.S. filing was matched by a Chinese complaint at the WTO against Commerce Department taxes targeting goods that the agency alleges are being “dumped” by China — sold at a below-market price to drive out competition.

While the top leaders of both countries have pledged to expand economic cooperation, the bureaucratic tussling has become frequent and intense. The Obama administration has steadily amped up its enforcement actions against China at the WTO, adding a new China unit in the Office of the U.S. Trade Representative and pulling in expertise from the State Department and other agencies to bolster its Mandarin language and other research capabilities.

The United State has typically fared well at the Geneva-based body, winning most of the cases it has brought against China. But the process can drag on, and the benefits to industry are sometimes disappointing. In some cases, dispute panels have produced settlements that allowed better market access. In others, the lag between the start of a particular Chinese policy and a WTO ruling against it has given China time to protect and build its national champions.

The auto industry has been at the center of trade troubles between the two nations before. The United States won an earlier case against import tariffs that China had imposed on American-made auto parts. But auto industry officials say the victory did little to stop the dispersion of auto parts manufacturing around the world. In July the administration challenged Chinese import duties on American-made cars; China was alleging that the government bailout of General Motors amounted to unfair underwriting of auto production.

That case also had political resonance even though its impact on American workers is expected to be minimal. The U.S. exports only 120,000 or so vehicles a year to China, and they are typically luxury models such as South Carolina-made BMWs, for which price is less of an issue for buyers.

A recent Commerce Department study said that with the auto industry still restructuring globally and with strong competition from Japan, Korea and elsewhere — as well as China — perhaps 10 percent of the country”s 5,000 auto parts makers “will fail in the next few years.”

The auto industry overall accounts for about 675,000 U.S. jobs. While it is unclear how much the elimination of the alleged Chinese subsidies might aid U.S. companies, a senior administration official said the aim is to continue mounting such challenges “as we’re able to peel away the intricacies” of China’s economic system. The policies targeted Monday include alleged tax breaks and preferential loan terms offered at a provincial level for firms located at “export bases.”

The United States runs a large and steady trade deficit with China — typically from $25 billion to $30 billion monthly. While the Obama administration has focused on the country’s potential as a large and growing market for U.S. exports, there has been concern that China’s membership in the WTO — which helped open U.S. markets to its goods — siphoned off middle-income manufacturing jobs as companies relocated to China to take advantage of the lower wages. China has tried to push its manufacturing expertise into increasingly sophisticated areas, seeking to challenge nations such as the United States, Japan, Korea and Germany as a manufacturer of high-tech equipment and industrial goods.

The timing of Monday’s action meshed with a campaign swing through Ohio, where Obama has heavily promoted the auto industry bailout he inherited from President George W. Bush and then ramped up in 2009. The industry directly employs 54,200 in Ohio, where unemployment lags the national average.

Major unions lauded the latest trade action.

“This isn’t just some political moment; this is part of a pattern of action,” said United Auto Workers President Bob King. The United Steel Workers union also released a statement praising the latest trade enforcement effort.

Gardner reported from Ohio.