BEIJING — As China ratchets up pressure on Taiwan, the self-governing island it claims as its territory, the United States is cautiously starting to push back.

In recent months, Chinese strategic bombers have been conducting “island encirclement” flights, escorted by fighter jets. The Chinese government has discouraged tourism to Taiwan and imports of goods like fish over the past year and a half, hurting its economy. And China persuaded the island’s most important remaining diplomatic ally, Panama, to switch diplomatic recognition last summer from Taipei to Beijing.

Concern about Taiwan’s fate now appears to be building slowly in Washington, even as President Trump continues to seek China’s help on other issues. Through his first year in office, Mr. Trump pressed Beijing to put more pressure on North Korea to abandon its nuclear and ballistic missile programs, with limited success. He has also sought to limit China’s nearly $400 billion trade surplus with the United States, which has nonetheless continued to widen.

Against that backdrop, Washington has recently begun moving gradually to reinforce its ties to Taiwan, a vigorous democracy facing an increasingly authoritarian government in Beijing.