Two small businesses sued the Trump administration on Friday over the latest tariffs it has imposed around the world, touching off another legal battle that could redefine President Trump’s powers to wage a global trade war.

The new challenge concerned the tariffs that the government had put in place just hours earlier, covering more than 80 countries including Canada, Mexico and the 27 members of the European Union. The lawsuit, filed in a federal trade court, argued that the Trump administration had misused the law in its attempt to recreate the same system of duties that judges had already ruled illegal.

The plaintiffs in the case are Burlap and Barrel, a New York-based spice retailer, and Collective Horology, a California watch seller. They are represented by the Liberty Justice Center, a legal group that has successfully challenged Mr. Trump’s tariffs repeatedly in his second term.

Lawyers for the organization previously joined state officials in invalidating the president’s original roster of punishing, country-by-country duties at the Supreme Court in February, and they similarly succeeded against Mr. Trump’s temporary replacement for those tariffs in the spring. The Liberty Justice Center has won over judges with arguments that Mr. Trump has violated the Constitution by usurping tariff powers reserved for Congress.

At the heart of the most recent fight is Mr. Trump’s use of Section 301 of the Trade Act of 1974. In general, the provision of law allows the government to investigate other countries’ trade practices, and it permits the president to impose tariffs on those that are found to behave unfairly.

Generally, Section 301 is understood to be settled policy, unlike some of Mr. Trump’s earlier tariff actions, which relied on novel interpretations of federal law. In fact, the president’s use of Section 301 to impose duties on Chinese goods during his first term survived several court challenges.

But small businesses said that Mr. Trump had stretched the statute beyond its limit this time, pointing to the way that his administration conducted its investigations — and the fact that it had planned to impose tariffs even before its reviews concluded.

One of the investigations specifically concerned claims that other countries had failed to crack down on “forced labor,” which had left U.S. businesses that follow such laws prohibiting coercive practices at a disadvantage. In June, the administration said it found fault in 86 countries, including U.S. allies that have laws banning forced labor practices. The tariffs it levied on Friday range between 10 percent to 12.5 percent, with little differentiation based on the country or its labor laws.

Canada, which has a law prohibiting forced labor, faces a 10 percent tariff on its exports. China, which U.S. officials frequently criticize for using forced labor, is subject to a tariff that is only 2.5 percent higher. Foreign officials say they have also received assurances from the United States that their tariff rates will be the same as they were under the trade deals they previously negotiated.

In response, lawyers for the two small businesses argued in their lawsuit that Jamieson Greer, the U.S. trade representative, did not adequately investigate each country. They contend that the administration had erred by studying the countries and issuing its findings and subsequent tariffs in bulk.

The opponents also pointed to past statements from Mr. Trump and his deputies, who had said they hoped to use Section 301 to replicate the tariffs declared illegal previously by the courts. That, according to the lawyers, suggested that the outcome of the investigations were predetermined, not based on the facts uncovered.

“Those statements, in combination with the timing, scope and rate structure of the final action, support the inference that the Section 301 tariffs, by design, replace the invalidated global tariff regime rather than constitute measures selected to obtain elimination of identified economy-specific practices,” they argued in their lawsuit.

Lawyers for the Liberty Justice Center said it was not clear how taxing imports on such a wide set of goods would help to change other countries’ labor practices. And they said the scope of the administration’s efforts raised constitutional concerns, arguing that a blessing by the court would greatly expand Mr. Trump’s power to impose tariffs without Congress.

“Forced labor is morally indefensible, but an important objective does not give the government permission to ignore the law,” said Sara Albrecht, the chairman and chief executive of the center. “The administration allowed one global tariff to expire and immediately replaced it with another under a different statute. Changing the statute doesn’t change the law.”

The White House did not respond to a request for comment.

When asked if any country could take action that would fully remove the tariffs, a senior administration official said Thursday that the government welcomed countries to take action but that the tariffs probably could not be “eliminated overnight.”

The official said that it was “too simplistic” to say the new tariffs replicated the ones struck down by the Supreme Court, and that they differed in important ways. But the official added that Mr. Trump would always use the tools at his disposal to achieve his trade policy goals, and that the president was not going to allow his trade policy to be undermined simply because one tool was limited by a court.

The case will send Mr. Trump and his opponents back to the Court of International Trade, a specialized federal circuit that has repeatedly found that the administration exceeded its power under law. The past fights have been tense, evident in the continuing battle over the roughly $160 billion that the government owes to importers who paid illegal tariffs imposed under the International Emergency Economic Powers Act.

Once again, states opposed to Mr. Trump’s tariffs could soon join the fight. Dan Rayfield, the attorney general of Oregon, said he was “reviewing the latest action to determine next steps.”

Citing Mr. Trump’s past tariff defeats, he criticized the president for “trying yet another way to impose the same costs on working families who are already struggling to get by.”

More duties are expected from Mr. Trump in the coming weeks, some of which could be affected by the new legal battle. The administration has explored a second tranche of tariffs using Section 301, targeting 15 countries and the European Union to offset what the White House calls unfair practices in their manufacturing sectors. And Mr. Trump on Friday said the government would open still another investigation into the European Union over its practice of fining U.S. tech companies.

The administration also invoked this week an obscure law to impose a 50 percent tariff on billions of dollars of Canadian exports. In that case, the president relied on a portion of the statute that has never been used to impose duties. That provision will not go into effect for 30 days. If it ultimately does go into effect, legal experts said it was also likely to be challenged.