Two state-run newspapers, The Global Times and China Daily, each ran pieces that directly called out Trump.
Without challenging the Chinese stance openly, the U.S. has maintained strong unofficial ties with Taiwan, including trade and weapons sales.
It said his latest comments appeared to show he meant to use the One China policy as a "trump card" and "bargaining chip".
Former Australian prime minister Paul Keating said Tillerson was threatening to involve Australia in a war with China, describing his comments as "simply ludicrous".
A rising China is a fact.
"I would not have expected it to be so soft", said Yan Xuetong, dean of the Institute of Modern International Relations at Tsinghua University. China has voiced its fury with the president-elect, Donald Trump, since he spoke by phone with Tsai after his election win.
A Chinese state-owned paper has blasted Donald Trump for "playing with fire" after the USA president-elect appeared to question the One China policy again.
THE Philippines will not stop the United States if it plans to block China from artificial islands in the contested West Philippine Sea (South China Sea), Foreign Secretary Perfecto Yasay Jr. said on Saturday.
In response, China this weekend insisted that Beijing treats its claimed ownership of Taiwan as "non-negotiable", saying "there is but one China in the world, and Taiwan is an inalienable part of China".
The Asian giant said it could back "forces hostile to the US" if Trump followed through with his threats.
'Therefore, there's no need for China to take his remarks seriously or further respond to what he said'.
In the past, Mr Trump has said he would label China a currency manipulator after he takes office. He has also pledged to impose high, retaliatory tariffs on China that economists say would all but guarantee a trade war.
It would be good if after his inauguration Trump can demonstrate more statesmanship.
"Once we start correcting the military imbalance, I actually think you will get more cooperation rather than less", the Trump adviser said.
The scathing piece was accompanied by a cartoon of Mr Trump brandishing a hand grenade labelled "Trump's China Policy". Those include USA pressure on Beijing to curb cyber hacking of United States entities. However, Trump has made no qualms about his desire to fix the US-Russia relations, which have taken a nosedive during recent years.
After attacking China repeatedly during his campaign, Trump has continued to disparage China on Twitter over its military build-up in disputed areas of the South China Sea, allegedly manipulating its currency to put American companies at a disadvantage, and not doing enough to curb North Korea's nuclear program.
"This does not bode well at all".