EU Health Ministry officials met in Brussels on Tuesday and reached the consensus.
The ministers will hold a crisis meeting on Wednesday to decide what co-ordinated measures will be applied across the bloc.
The gatherings were called after China decided to lift its "zero-Covid" policy, which has sparked massive demand for flights abroad by Chinese citizens and residents who had been grounded for nearly three years.
The EU fears a sudden influx of passengers from China could bring Covid variants that may be able to evade current vaccines.
There are also concerns that China's data on infections is incomplete and insufficient.
China Covid latest - in pictures
EU health commissioner Stella Kyriakides said the officials also agreed to recommend increased monitoring of wastewater from flights and at airports to detect traces of the coronavirus, and for member states to boost surveillance.
Ms Kyriakides stressed the need for EU "unity" at the meeting to take place on Wednesday.
Earlier on Tuesday, the commission said an "offer stands" for the EU to provide Covid-19 vaccines and expertise to China.
A spokesman said Ms Kyriakides had repeated the vaccine offer recently and that any supply of them was dependent on Beijing's reaction.
Many EU countries have a surplus of mRNA vaccines — especially the one made by BioNTech/Pfizer — that scientific studies have shown to be more effective against severe Covid than the inactivated-virus drugs China has developed and uses.
Italy starts testing for Covid-19 among travellers from China - in pictures
Austria to test wastewater from flights from China
"Starting next week, Austria will examine samples from the wastewater from aircraft from China," Austria's Health Ministry said.
It said wastewater from the sewage plant in the picturesque village of Hallstatt — a top Chinese tourist destination — would also be analysed.
This is in addition to testing wastewater in the cities of Vienna and Salzburg, which is already being monitored as part of a national programme launched at the start of last year.
"With this, some places frequently visited by tourists from China are regularly examined," the ministry said.
"This makes it possible to discover new virus variants, even if visitors from China have not entered the country with direct flights."
Covid patients fill ICUs in China's hospitals - video
Tests on passengers 'unacceptable', says China
China on Tuesday called the increasing international restrictions on travellers from its territory "unacceptable".
China's steep rise in infections comes after Beijing abruptly lifted years of hardline restrictions last month, with hospitals and crematoriums quickly overwhelmed.
But Beijing has pushed ahead with a long-awaited reopening, last week announcing an end to mandatory quarantine on arrival in a move that prompted Chinese people to plan trips abroad.
"Some countries have taken entry restrictions targeting China," foreign ministry spokeswoman Mao Ning said.
"This lacks scientific basis and some practices are unacceptable.
Ms Mao said that China could "take counter-measures based on the principle of reciprocity".
Covid symptoms - in pictures
The US replied that it had acted in response to the "lack of adequate and transparent" data from China, and concerns that the heavy caseload could give birth to new variants.
"This is an approach that is based solely and exclusively on science," State Department spokesman Ned Price said in Washington.
France's Prime Minister, Elisabeth Borne, defended the new rules.
"I think we're performing our duty in asking for tests," Ms Borne told franceinfo radio. "We will continue to do it."
The rules affect all travellers coming from China, not just Chinese nationals, while Beijing continues to restrict inbound visitors and not issue visas for tourists or international students.