The state-run Chinese tabloid Global Times warned US President-elect Donald Trump that China would "take revenge" if he reneged on the one-China policy.
Taiwan President Tsai Ing-wen met senior US Republican lawmakers during her stopover in Houston on Sunday en route to Central America.
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. China is deeply suspicious of Tsai, who it thinks wants to push for the formal independence of the island.
A photograph tweeted by Texas Governor Greg Abbott shows him meeting Tsai. 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.
"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."
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 US commitment to China's position that Taiwan is part of one China.
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 U.S. officials and engaging in activities that interfere with and damage China-U.S. relations," Lu said.
Taiwan's President Tsai Ing-wen, left, and First Vice President of Honduras Ricardo Alvarez stand at attention for the playing of national anthems, after Tsai's arrival at Soto Cano Air Base outside Comayagua, Honduras on Sunday. Image: Fernando Antonio AP/Press Association Images
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.