Ahead of President Trump’s next big trade move, his administration invited companies to weigh in on the economic barriers they faced abroad.

       The list of complaints was both sprawling and specific. In hundreds of letters submitted to the administration in recent weeks, producers of uranium, shrimp, T-shirts and steel highlighted the unfair trade treatment they faced, in hopes of bending the president’s trade agenda in their favor. The complaints varied from Brazil’s high tariffs on ethanol and pet food, to India’s high levies on almonds and pecans, to Japan’s longstanding barriers to American potatoes.

       Mr. Trump has promised to overhaul the global trading system on April 2, when he plans to impose what he is calling “reciprocal tariffs” that will match the levies and other policies that countries impose on American exports. The president has taken to calling this “liberation day,” arguing that it will end years of other countries “ripping us off.”

       On Monday, Mr. Trump appeared to suggest a potential softening to the tariffs, saying, “I may give a lot of countries breaks.” He added, “It’s reciprocal, but we may be even nicer than that.”

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       “They’ve charged us so much that I’m embarrassed to charge them what they’ve charged us,” he said at an event at the White House. “But it’ll be substantial.”

       Mr. Trump also signaled that the White House could finalize tariffs on foreign-made cars before April 2, teasing that an announcement could come “fairly soon, over the next few days probably.”

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