WASHINGTON—Donald Trump’s pledge to declare China a currency manipulator on day one of his presidency raises the prospect of U.S. tariffs on the Asian giant that figure to push their relationship onto new, contentious ground.

The threat, which Mr. Trump has made repeatedly, risks sparking a trade war with China that would complicate negotiations on a host of other strategic and economic issues. It also risks sparking a legal backlash by U.S. importers.

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