Taiwan President Tsai Ing-wen met senior US Republican lawmakers during her stopover in Houston on Sunday en route to Central America, where she will visit Honduras, Nicaragua, Guatemala and El Salvador. Tsai will stop in San Francisco on Jan 13, her way back to Taiwan.
China had asked the United States not to allow Tsai to enter or have formal government meetings under the one China policy.
Beijing considers self-governing Taiwan a renegade province ineligible for state-to-state relations. The subject is a sensitive one for China.
A photograph tweeted by Texas Governor Greg Abbott shows him meeting Tsai, with a small table between them adorned with the US, Texas and Taiwanese flags. Tsai's office said on Monday she also spoke by telephone with US senator John McCain, head of the powerful Senate Committee on Armed Services. Tsai also met Texas Senator Ted Cruz.
"Sticking to (the one China) principle is not a capricious request by China upon US presidents, but an obligation of US presidents to maintain China-US relations and respect the existing order of the Asia-Pacific," said the Global Times editorial on Sunday. The influential tabloid is published by the ruling Communist Party's official People's Daily.
Trump triggered protests from Beijing last month by accepting a congratulatory telephone call from Tsai and questioning the U.S. commitment to China's position that Taiwan is part of one China.
"If Trump reneges on the one-China policy after taking office, the Chinese people will demand the government to take revenge. There is no room for bargaining," said the Global Times.
Cruz said some members of Congress had received a letter from the Chinese consulate asking them not to meet Tsai during her stopovers.
"The People's Republic of China needs to understand that in America we make decisions about meeting with visitors for ourselves," Cruz said in a statement. "This is not about the PRC. This is about the US relationship with Taiwan, an ally we are legally bound to defend."
Cruz said he and Tsai discussed upgrading bilateral relations and furthering economic cooperation between their countries, including increased access to Taiwan markets that would benefit Texas ranchers, farmers and small businesses.
Chinese Foreign Ministry spokesman Lu Kang on Monday urged "relevant US officials" to handle the Taiwan issue appropriately to avoid harming China-US ties.
"We firmly oppose leaders of the Taiwan region, on the so-called basis of a transit visit, having any form of contact with US officials and engaging in activities that interfere with and damage China-US relations," Lu said.
In a dinner speech Saturday to hundreds of overseas Taiwanese, Tsai said the United States holds a "special place in the hearts of the people of Taiwan" and that the island via bilateral exchanges has provided more than 320,000 jobs directly and indirectly to the American people, her office said on Monday.
Tsai said Taiwan looked to create more US jobs through deeper investment, trade and procurement.
Tsai's office said James Moriarty, chairman of the American Institute in Taiwan, which handles US-Taiwan affairs in the absence of formal ties, told the Taiwan president in Houston that the United States was continuing efforts to persuade China to resume dialogue with Taiwan.
China is deeply suspicious of Tsai, who it thinks wants to push for the formal independence of the island.
The Global Times, whose stance does not equate with government policy, also targeted Tsai in the editorial, saying that the mainland would likely impose further diplomatic, economic and military pressure on Taiwan, warning that "Tsai needs to face the consequences for every provocative step she takes".
"It should also impose military pressure on Taiwan and push it to the edge of being reunified by force, so as to effectively affect the approval rating of the Tsai administration."