WASHINGTON—President Trump ratcheted up pressure on Chinese trade negotiators, saying the U.S. was moving ahead with fresh levies on everything China sells to the U.S. that isn’t already subject to tariffs.

The president’s comments came hours before high-level trade talks aimed at salvaging a deal began Thursday evening. Mr. Trump said the U.S. was “starting the paperwork” to impose 25% tariffs on $325 billion in Chinese goods that aren’t currently taxed.

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