In 2016, Taiwan’s president called Donald J. Trump to congratulate him after he won the presidential election. Mr. Trump took the call, becoming the first American president or president-elect to speak to a Taiwanese leader in decades.

This time, after Mr. Trump won a second term in the White House, Taiwan was quick to deny reports that its current leader, Lai Ching-te, was seeking a similar phone call with the president-elect.

The contrast was telling.

Taiwan appears to be preparing for a more delicate, possibly testy, relationship with Mr. Trump upon his return to the White House. On the campaign trail, Mr. Trump had suggested that Taiwan should pay the United States for helping defend the island from China, and complained that Taiwan had stolen America’s business in semiconductors.

“There is more anxiety this time” in Taiwan about Mr. Trump’s taking office, Chen Ming-chi, a former senior adviser on Taiwan’s National Security Council, said in an interview.

By “declaring that we are not going to seek a congratulatory phone call, that means we are more realistic,” said Professor Chen, who teaches at Taiwan’s National Tsing Hua University. Mr. Lai issued a congratulatory statement about Mr. Trump’s victory.

Tensions between Beijing and Taipei are high, with frequent Chinese military drills stoking fears of an accidental conflict. A call with Mr. Trump could prompt a forceful reaction from China, which claims the island as its territory and resents whenever Taiwan acts like, or is treated as, a sovereign nation.