President Donald Trump’s planned tariffs on steel and aluminum threaten a world-trading regime already battered by mounting protectionism and its struggle to tame China’s state-driven capitalism.

Mr. Trump is expected to sign a proclamation this week outlining his plan to impose the tariffs, which have angered close U.S. allies. European Union officials have suggested they could impose up to $3.5 billion in retaliatory tariffs on U.S. products almost immediately.

The plan to slap duties of 25% on steel imports and 10% on aluminum, citing national security concerns, is forcing members of the World Trade Organization to grapple with flaws and weaknesses in the global body. The U.S. helped establish the WTO in 1995, but Mr. Trump has attacked it since before his campaign as broken and working against U.S. interests.

Even WTO supporters concede they face a difficult choice: Challenge the U.S. using WTO rules and risk exposing it as inadequate to the task, or circumvent its rules and risk destroying the whole institution.

The conundrum is embodied in the EU’s rapid response plan, which Brussels says would be legal but some Europeans fear would enter uncharted territory by leveling retaliatory duties without a WTO ruling.