The World Trade Organization gave China the go-ahead on Friday to impose sanctions on up to $3.6 billion of American goods in a fight over unfairly cheap Chinese goods, a decision that is likely to further inflame the Trump administration’s antipathy toward the global trade body.

The ruling is the final decision in a case China brought against the United States nearly six years ago that stemmed from levies placed on more than 40 Chinese goods. The duties were imposed during the Obama administration, but the practice they were intended to curb remains one of the Trump administration’s biggest economic concerns about China.

At issue are subsidies that the United States has accused China of providing to its companies so that they can sell goods more cheaply overseas. To stop China from flooding the American market with dozens of low- cost Chinese products — including solar panels, furniture, shrimp, steel pipe, tires and washing machines — the United States imposed “anti-dumping duties” on those goods.

A 2017 decision by the World Trade Organization found that the United States had not followed the global trade body’s rules in the way it imposed the duties. On Friday, the W.T.O. gave China the green light to try to recoup some of the losses it sustained by imposing enough tariffs on American goods to block $3.6 billion worth of American exports to China.