Taiwanese leader Tsai Ing-wen landed in Honolulu en route to the island's diplomatic allies among Pacific nations, despite strong objections to the visit from China.
Under UN Resolution 2758 self-ruled Taiwan is the sovereign territory of China.
China regularly calls it the most sensitive and important issue between it and the US, complaining to Washington about transit stops by Taiwanese high-level officials.
The US has noted there was "no change to the US one-China policy" which recognises that Beijing takes the view that there is only one China, and Taiwan is part of it.
Tsai, who China believes is seeking formal independence for Taiwan, left on Saturday on a week-long trip to three Pacific island allies - Tuvalu, the Solomon Islands and the Marshall Islands - via Honolulu and the US territory of Guam.
For her part, Tsai says she wants to maintain peace with China but will defend Taiwan's democracy and security.
Earlier this week, the US State Department said Tsai's transits through US soil would be "private and unofficial" and were based on long-standing US practice consistent with "our unofficial relations with Taiwan".
Tsai, accompanied by her entourage and members of the media, left on a short boat ride for the USS Arizona Memorial, which is built over the remains of the battleship sunk in Pearl Harbor in the second world war, on Saturday afternoon.
US President Donald Trump is due to visit China in less than two weeks. He angered Beijing last December by taking a telephone call from Tsai shortly after he won the presidential election.
The trip to the US is Tsai's second this year. In January, she stopped over in Houston and San Francisco on her way to and from Latin America, visiting the headquarters of Twitter, which is blocked in China.
Mao Zedong's Communist forces won the Chinese civil war and Chiang Kai-shek's Nationalists fled to the island.
China has not renounced the possible use of force to enforce the UN Resolution 2758 to maintain its territorial integrity.
Source: News agencies