France and Spain have announced Covid testing on visitors from China, following a similar decision in Italy.
The French government said passengers flying from China to France would have to present a negative Covid test less than 48 hours old before embarking.
Arrivals in Spain can skip the tests if they are fully vaccinated – and Spain does accept some Chinese vaccines.
Beijing has said it will fully reopen its borders next week for the first time since March 2020.
Its current Covid surge has caused wariness, with reports of hospitals filling up and waves of illness.
The UK, South Korea and Israel also announced new testing rules on Friday, while the US and India have already imposed restrictions.
“At the national level, we will implement controls at airports and require travellers from China to present a negative Covid test or be fully vaccinated,” said Spanish health minister Carolina Darias.
Neither France nor Spain have specified when the measures will come into force.
However, the French health and transport ministries said the government would publish a decree and notify EU member states.
On Thursday, the EU’s disease prevention agency has said such measures were not justified in Europe, because of the levels of immunity and the fact that variants spreading in China were already present on the continent.
The World Health Organization, however, has said it was “understandable” that some countries had decided to impose restrictions and urged Beijing to be more forthcoming about its Covid numbers.
China’s foreign ministry said earlier this week that its “epidemic situation” overall was “predictable and under control”.
But the true toll of daily cases and deaths in China is unknown as officials have stopped requiring cases to be reported, and changed classifications for Covid deaths.
South Korean Prime Minister Han Duck-soo said that travellers from China would need to have a negative PCR or antigen test before boarding flights to South Korea.
They will also need to undergo a PCR test within the first day of their arrival in South Korea.
Israel, meanwhile, has ordered foreign airlines not to allow people to travel from China unless they have tested negative – and asked its own citizens to avoid unnecessary travel there.
Not all countries have announced controls. Germany has joined Australia, France, and Portugal in saying there will be no new rules yet.
However, Germany’s health minister has said the country is seeking a co-ordinated system to monitor variants across European airports.
China’s decision this week to reopen its borders on 8 January marks the last stage of the country’s controversial zero-Covid policy, which President Xi Jinping had personally endorsed.
As the rest of the world transitioned to living with the virus, Beijing maintained an eradication policy involving mass testing and stringent lockdown.
In November, the frustration spilled on to the streets in rare protests against Mr Xi and his government. A week later, Beijing began to roll back the restrictions.