China, which claims democratically-governed Taiwan as its territory despite the Taipei government's strong objections, has been executing war games and drills near Taiwan since U.S. House Speaker Nancy Pelosi made a two-day visit to Taipei earlier this month.
Last week the second group of U.S. lawmakers visited Taiwan.
Governor Eric Holcomb tweeted that he would visit South Korea, while Taiwan's presidential office announced he would meet President Tsai Ing-wen on Monday morning.
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"I'm energized to spend this week building new relationships, reinforcing long-time ones, and strengthening key sector partnerships with Taiwan and South Korea," Holcomb tweeted.
He termed his visit to Taiwan and South Korea an "economic development trip," stating he was the first U.S. governor to come to Taiwan since the COVID-19 pandemic started over two years ago.
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"Our delegation will spend this week meeting with government officials, business leaders, and academic institutions to strengthen Indiana's economic, academic and cultural connections with Taiwan and South Korea," Holcomb announced in a tweet.
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There was no immediate response from China to his arrival.
Taiwan's Foreign Ministry announced Holcomb would further meet representatives from Taiwanese semiconductor companies, although it gave no details, and would sign various trade and technology memorandums of understanding.
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Taiwan is home to the world's largest contract chip maker, Taiwan Semiconductor Manufacturing Co Ltd (TSMC) , which is building a $12 billion plant in the U.S. state of Arizona.
China states Taiwan is the most important and sensitive matter in its relations with Washington and that it considers anything to do with the island an internal matter.
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Taiwan's government states that as the People's Republic of China has never ruled the island, it has no right to claim it, and that just Taiwan's 23 million people can decide their future.
China's military drills have been proceeding around Taiwan, though on a smaller scale than the war games conducted immediately after the trip by Pelosi, the highest level U.S. official to visit in decades.
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Taiwan's defense ministry stated that 12 Chinese aircraft and five Chinese ships were detected operating around Taiwan on Sunday, including five aircraft that crossed the Taiwan Strait median line, as Beijing continued military activities near the island.
Meanwhile, Chinese president Xi Jinping reportedly asked his US counterpart Joe Biden to stop house speaker Nancy Pelosi from visiting Taiwan throughout a phone conversation in July.
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