When President Trump announced his first round of tariffs across most of the world in April, Taiwan looked like it was in a good bargaining position.

The company at the heart of Taiwan’s economy, Taiwan Semiconductor Manufacturing Company, which makes the world’s most advanced computer chips for companies like Nvidia and Apple, had only weeks earlier said it would spend $100 billion to expand its operations in Arizona. As Mr. Trump ran down the list of new tariff rates, he singled out Taiwan to praise TSMC for the investment.

“One of the great companies of the world actually, they’re coming in from Taiwan and they’re going to build one of the biggest plants in the world, maybe the biggest, for that,” Mr. Trump said.

This week it emerged that TSMC’s investment may earn the company an exemption from 100 percent tariffs on semiconductors. But it has not been enough to help Taiwan’s leaders clinch a trade deal with Washington and shield their economy from Mr. Trump’s other punishing tariffs.

The 20 percent tariffs on Taiwan, which took effect on Thursday, add to the mounting political and economic pressure facing Taiwan’s president, Lai Ching-te, who was elected in January 2024. He is facing an intensifying confrontation with opposition lawmakers able to effectively stymie his policies. And Taiwan’s currency has appreciated sharply this year against the U.S. dollar — a hindrance for an economy so heavily dependent on exports.

Taiwan’s lead trade negotiators, Vice Premier Cheng Li-chiun and the chief trade representative, Yang Jen-ni, have gone to Washington four times since April. They have yet to reach a deal while neighboring Japan and South Korea have negotiated lower tariff rates than Taiwan, further weakening the competitiveness of the island’s exports.