China considers self-governed Taiwan to be part of its territory and opposes any international recognition of the island and its claim to be a sovereign state.
Beijing especially bristles at official exchanges between Taiwan and the United States, which does not recognize Taipei diplomatically but is its most important backer and biggest supplier of arms.
Lai, who has been an outspoken defender of Taiwan's sovereignty and whom Beijing calls a "separatist," is on his first overseas trip since taking office in May.
He landed in the US island state of Hawaii shortly before 7:30 am local time (1730 GMT), said an AFP journalist traveling with the president for the duration of the trip.
Lai was met at Honolulu International Airport by Ingrid Larson, who is the managing director in Washington of the American Institute in Taiwan, and Hawaii Governor Josh Green.
"This is the first time the (Taiwan) head of state was greeted on the tarmac, given red carpet treatment and presented with flowers, marking the highest standard of courtesy over the past years, in a departure from the traditional terminal reception protocol," Taipei's Presidential Office said in a statement.
Lai will have a two-day stopover in Hawaii, with visits on Saturday to the Bishop Museum, Hawaii Emergency Management Agency, and the USS Arizona Memorial at Pearl Harbor, according to his official schedule.
He will later spend one night in the US territory of Guam as he visits Taiwan's allies Marshall Islands, Tuvalu and Palau.
They are the only Pacific island nations among the 12 remaining countries that recognize Taiwan, after China poached others with promises of aid and investment.
In a speech shortly before departing Taipei, Lai said the trip "ushered in a new era of values-based democracy" and he thanked the US government for "helping to make this trip a smooth one."
Lai said he wanted to "continue to expand cooperation and deepen partnerships with our allies based on the values of democracy, peace and prosperity."
Threat of invasion
Taiwan lives under the constant threat of an invasion by China, which has refused to rule out using force to bring the island under its control.
Beijing deploys fighter jets, drones and warships around Taiwan on a near-daily basis to press its claims, with the number of sorties increasing in recent years.
Taiwanese government officials have previously stopped over on US soil during visits to the Pacific or Latin America, angering China, which has sometimes responded with military drills around the island.
In a swift response to news of Lai's trip on Thursday, Wu Qian, a spokesperson for China's defence ministry said "we firmly oppose official interaction with China's Taiwan region in any form" and vowed to "resolutely crush" any attempts for Taiwan independence.
Lai's trip follows the US approval on Friday of the proposed sale to Taiwan of spare parts for F-16 fighter jets and radar systems, as well as communications equipment, in deals valued at $385 million in total.
The dispute between Taiwan and China dates back to 1949, when Chiang Kai-shek's nationalist forces were defeated by Mao Zedong's communist fighters and fled to the island.
The two have been ruled separately ever since, with Taiwan developing into a vibrant democracy and a powerhouse in the semiconductor industry.
China has sought to erase Taiwan from the international stage, blocking it from global forums and assiduously whittling down its allies.
Lai's tour of the Pacific was an opportunity for him "to show those countries and the world that Taiwan matters," said Bonnie Glaser, a Taiwan-China affairs expert at the German Marshall Fund of the United States.
"Having some countries in the world recognize that claim to sovereignty is part of what is considered important in order for that claim to remain valid," Glaser told AFP.
