US President Donald Trump, who was inaugurated on Friday, said in December the United States did not necessarily have to stick to its long-standing position that Taiwan is part of "one China".
Earlier, Trump broke with decades of precedent by taking a telephone call from Taiwan President Tsai Ing-wen, Reuters reported
According to Beijing's one China principle, Taiwan and mainland China are inalienable parts of a single "China". Beijing views Taiwan as a wayward province, to be brought under its control by force if necessary.
However, proudly democratic Taiwan shows not interest in being ruled by Beijing.
"We urge the new administration to fully understand the high sensitivity of the Taiwan issue and to continue pursuing the one China policy," Chinese foreign ministry spokeswoman Hua Chunying told a regular briefing in Beijing.
Hua called the policy the "political foundation" of future relations between the United States and China.
She said any US Government had the obligation to stand by the promises made by both main US political parties and "strictly" maintain non-diplomatic relations with Taiwan.
Hua also reiterated China's position on the South China Sea, saying the United States should not meddle in issues of China's sovereign territory.
Both "history and reality" prove good relations between China and the United States were positive for the Asia-Pacific region, she said.
China claims most of the energy-rich South China Sea through which about $5 trillion in ship-borne trade passes every year. Neighbors Brunei, Malaysia, Taiwan and Vietnam also have claims.
US Secretary of State nominee Rex Tillerson has previously suggested that China would not be allowed access to islands in the region, prompting Chinese state media to say the United States would need to "wage war" to cut off China's access.