When President Trump announced he would impose new tariffs on imports from countries around the world, he launched a frontal attack on the global free trade system created in the aftermath of World War II.

Mr. Trump’s move, announced Thursday and set to begin as soon as April, represents a bet that the United States will gain leverage by replacing global tariffs with its own tariffs, which are taxes on imports.

The United States, the world’s largest importer, has for decades bought far more from the rest of the world than it sells. Mr. Trump wants to change that and is calculating that other countries, with more exports at stake, might be cautious about retaliating by raising their own tariffs.

But instead, many trade experts warn, Mr. Trump’s action could presage a global shift toward higher tariffs. That would pose a big challenge to the World Trade Organization, which was established in 1993 to coordinate global tariffs and trade rules.

Decisions by other countries to follow Mr. Trump’s example and set tariffs unilaterally could impede trade, raising prices for everyone. The free trade promise of consumers buying from the lowest-cost producers could be imperiled.

“I would say the W.T.O. is toast, but what matters now is how other members respond,” said Deborah Elms, the head of trade policy at the Hinrich Foundation, a research group in Singapore that favors free trade. “Do they stand up for the system? Or do they also ignore key principles, provisions and practices?”