After Beijing said it would reopen borders next week, the US became the latest country to impose Covid testing on Chinese visitors.
There were no new rules for travellers from China according to Australia and the UK.
China will allow people to travel more freely from 8 January.
Wariness has been caused by the country's Covid surge.
According to analysts, the daily case load in China may be close to a million. Hospitals are overwhelmed and residents are having a hard time finding basic medicines.
On Wednesday, the US said a lack of "adequate and transparent" Covid data in China had contributed to the decision to require Covid tests for travellers from China, Hong Kong and Macau.
The US Centers for Disease Control and Prevention said this was needed to slow the spread of the virus.
On Wednesday, Beijing's foreign ministry accused Western countries and the media of hyping up the situation.
The people were angry on the social media.
All of the foreign countries have opened up. There was a comment that was liked 3000 times. Anyone coming from China or a third country must be tested according to the US.
"This is nothing compared to all the restrictions we had for people coming into China," one person wrote.
Travelers will be able to travel in and out of the country for the first time in over a year after Beijing announced on Monday that it was ending theQuarantine for Arrivals. Anyone entering China had to go through a state facility.
China was the largest outbound tourism market before the Pandemic. It's not clear how many Chinese people will travel abroad after 8 January due to the limited number of flights and the need for passports.
The UK and Australia said they were not planning on announcing new testing requirements but were monitoring the situation.
Others have announced restrictions quickly.
The EU's health security committee will meet on Thursday to discuss possible measures for a coordinated EU approach to China's Covid surge.
Italy, an EU member state and an epicenter of the virus, said it was moving first to "ensure the surveillance and identification" of any new variant of the virus.
Passengers from China were being tested on flights arriving in Milan. More than half of the passengers on the flight were found to have Covid.
The Prime Minister said that 15 of the people arriving from China had Omicron variant that were already present in Italy. The news was reassuring to her.
Italy is one of 26 European countries in the border-free Schengen zone and Ms Meloni is calling for EU-wide testing of Chinese passengers.
China's foreign ministry stated that the epidemic situation in China is under control.
The true toll of daily cases and deaths in China is not known as officials have stopped requiring cases to be reported. They stopped releasing daily case counts on Sunday.
According to Dr Chandrakant Lahariya, an Indian epidemiologist and health systems specialist, the increase in infections in China is expected.
The cases will rise if the population is not exposed to the virus. There has been no change for the rest of the world.
The reopening of China's borders marks the end of the country's zero-covid policy, which was endorsed by the president.
Beijing insisted on an eradication policy even after the rest of the world moved to living with the virus.
In November, when the economy took a hit and people became exhausted and angry, they took to the streets to protest. Beijing began to relax the restrictions.