Seven people tied to the news outlet were arrested and the government froze the outlet's financial assets.
"We urge [the U.S.] to discard the obsolete Cold War zero-sum mentality and ideological bias," Chinese Foreign Ministry Spokesperson Zhao Lijian said.
Telephone and online hotlines allow citizens to report others who talk about these 10 "rumours."
Taiwan's ruling party has "thrown itself into a political gamble that has only short-term benefits and no chance of winning in the long run," said the Global Times.
Trump could both box in his successor and solidify his recalibration of U.S.-China policy with one brilliant diplomatic move.
On Tuesday, the Senate unanimously agreed to a new bill fortifying U.S. support for Taiwan, which Beijing considers a future part of a unified China.
The Global Times warned that the U.S. would be "bound to pay the price" if it acts aggressively over Taiwan.
State media dismissed criticism after two Chinese fighter jets crossed the "middle line" between the mainland and Taiwan on Sunday.
Beijing and Washington vie for influence in the Asia-Pacific as China presses strategic regional goals.
Beijing faces a risk of a short-lived victory as "Trump will not want to be seen as having caved in.'
The successful intervention by Tillerson, suggests that in a White House-dominated administration, the new secretary of state could help drive decisions on some geopolitical issues.
The latest Chinese naval exercises have unnerved Beijing's neighbors, especially Taiwan which China claims as its own.
Beijing says the U.S.'s One China policy is the "bedrock" of the two countries' relationship.
The U.S. State Department said it had not been notified in advance of the ceremony and that it was inconsistent with U.S. policy.