TAIPEI, Taiwan — When China’s leader, Xi Jinping, sits down with President Donald Trump to address their worsening trade tensions, he will also be pursuing another, longer goal: persuading the American president to soften U.S. support for Taiwan.

Trump has said that he wants to focus on trade when he meets Xi in South Korea, even if the Chinese leader presses him on Taiwan, the democratically governed island roughly 100 miles off China’s coast that Beijing claims as its own.

But the diplomatic maneuvering raises a crucial question: how negotiable is American support for Taiwan, especially given Trump’s sometimes dismissive comments about the island? Chinese officials, analysts said, may seek at this and other meetings to draw Trump out on the issue, to have him clarify his position on Ta

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