European Commission President Ursula von der Leyen told a news conference after the meeting that the health situation in Europe was "very serious", with new variants and an increase in infections.
She stressed that countries should not close their borders, to ensure the functioning of the single market, including the flow of goods and travel for cross-border workers.
However, she said the Commission would add a new "dark red" category to its traffic light indications of risk, for regions where the virus was circulating at a very high rate. Today, almost all of Europe is red.
"Persons travelling from dark red areas could be required to do a test before departure, as well as to undergo quarantine after arrival," she said, adding all non-essential travel should be discouraged from these areas.
German Chancellor Angela Merkel said before the meeting that European countries needed to take the new mutation found in Britain seriously to avoid a third wave.
"We can't rule out border closures, but want to prevent them though cooperation within the European Union," she told a news conference in Berlin.
Alexander De Croo, prime minister of Belgium, where cases per capita are lower than in its neighbours, said he would ask fellow EU leaders to halt non-essential travel, such as tourism.
"The slightest spark could push the figures back up again. We need to protect our good position," he told broadcaster VRT.
Separately, the EU executive wants the 27 member states to agree a common approach to vaccination certificates by the end of January. So a certificate from Estonia would be accepted in Portugal, for example.
Greece and Spain have floated the idea that they could help restore cross-border travel.
However, French President Emmanuel Macron said vaccine passports needed to be looked at with "great caution", according to the Elysee, particularly because it was not yet clear if vaccinated people could still transmit the virus to others.
Charles Michel, the European Council president who chairs EU summits, said this would have to be a debate for later.
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