The three large steel makers are by far the most aggressive objectors in the exclusions process. Nucor and United States Steel have each filed more than 1,000 objections, some of which overlap. AK Steel has filed nearly 700 objections.

The department has granted more than 1,300 steel exclusions. More than 70 percent of those exclusions — nearly 1,000 of them — have gone to a single company that has managed to draw few objections to its requests: South Carolina-based Greenfield Industries, which makes drill bits, saw blades and other cutting tools. Since 2009, Greenfield has been owned by a Chinese company, Top-Eastern.

Steel makers’ objections to others’ requests take a variety of forms. Sometimes, the steel makers allege the company seeking an exclusion made an error in its filings. Sometimes, they criticize companies for choosing not to produce steel in the United States and instead buying it from overseas producers; one company’s decision to cease domestic production of steel slab “directly undermines U.S. steel production and should not be rewarded with the requested product exclusions,” Nucor wrote in a comment.

Often, the steel makers claim that an American mill is producing the product in question, or could produce it if asked. “Nucor can offer a substitute for the requested product out of stock immediately (i.e., within 8 weeks),” the company wrote in response to an exclusion request from Houston-based SEBA Tubular, which had sought to import steel bars from Turkey, citing insufficient supplies from American mills. “To the extent that further manufacturing is required, Nucor can ship/deliver the product within the above-referenced time frames.”

The SEBA request was denied. Company officials did not respond to a request for comment.

Mr. Ferriola, the Nucor chairman, said his company generally objects to exclusion requests if it produces the product in question or a substitute, or if it believes that granting the exclusion would undermine national security. “We should be able to compete against any steel maker in the world, but we cannot compete against those who dump artificially cheap steel into our market at prices that are lower than our cost of production,” he said. “That is why Nucor continues to assess market conditions, and will be proactive and aggressive in pursuing trade cases and objecting to exclusion requests, when and where it is appropriate.”

Asked if the company’s success in blocking exclusion requests was related to the investment in Mr. Navarro’s film, a company spokeswoman, Katherine Miller, said in an email that “as America’s largest steel producer, we have been actively engaged in the trade arena for almost two decades. Over this time, we have been outspoken that our government must take a much tougher line with countries that continuously violate the rules of free trade. The documentary produced seven years ago provided another medium to discuss this critical economic issue.”

A United States Steel spokeswoman, Meghan M. Cox, noted that the company has filed comments on “less than 10 percent of the total requests posted by the Commerce Department” and “only on those tariff exclusion requests that are for products that we make.”

“With the restart of one blast furnace earlier this year and preparations for another blast furnace restart in October underway at our Granite City Works,” Ms. Cox said, “we are willing and able to support substantial proportions of increased domestic demand for many steel products.”