A federal appeals court ruled on Friday that many of President Trump’s most punishing tariffs were illegal, delivering a major setback to Mr. Trump’s agenda that may severely undercut his primary source of leverage in an expanding global trade war.

The ruling, from the U.S. Court of Appeals for the Federal Circuit, affirmed a lower court’s initial finding in May that Mr. Trump did not possess unlimited authority to impose taxes on nearly all imports to the United States. But the appellate judges delayed the enforcement of their order until mid-October, allowing the tariffs to remain in place so that the administration can appeal the case to the Supreme Court.

The adverse ruling still cast doubt on the centerpiece of Mr. Trump’s trade strategy, which relies on a 1970s law to impose sweeping duties on dozens of the country’s trading partners. Mr. Trump has harnessed that law — the International Emergency Economic Powers Act, or IEEPA — to raise revenue and to pressure other countries into brokering favorable deals. The law has typically been reserved for sanctions and embargoes against other nations.

The loss proved especially stinging after the Trump administration told the court earlier on Friday that any weakening of its tariff powers could unleash economic chaos. Hours before the ruling, the president’s top economic advisers raised special concern about the fate of the trade agreements the United States had struck with other governments. Among the deals they cited was an agreement with the European Union, which made favorable concessions to escape even higher U.S. taxes on its goods.

The president, who has spent months insisting that his tariffs would make America “rich again,” has invoked the specter of the Great Depression if his ability to impose levies is curtailed and if the country is forced to pay back billions of dollars in tariff revenue.

In a social media post after the ruling on Friday, Mr. Trump blasted the court and its conclusions, and appeared to tee up a forthcoming appeal to the Supreme Court.