Leaders of the EU's 27 countries met online on Thursday at the start a two-day summit to discuss the pandemic.
“Everyone agreed that we need a digital vaccination certificate,” Angela Merkel, the German chancellor, told reporters after an EU virtual summit.
“This will make travelling within the EU possible and could pave the way for further travel from third countries into the EU.”
However, she said that it could take three months for the European Commission to set up the technology for such documents.
Greece already has digital vaccination certificates. Others such as Denmark and Sweden have talked about developing them.
Greek Deputy Prime Minister Akis Skertsos said that non-vaccinated tourists could also visit Greece this summer.
However, speaking to the BBC, he said the procedure for them would be slower as they would need to be tested and might have to self-isolate on arrival.
Spain has also been pushing to establish an EU-wide vaccine passport policy.
Spanish foreign minister Manuel Muñiz proposed that vaccine certificate holders could be exempt from taking a Covid test.
He said that establishing EU-wide rules would “protect mobility in line with all health criteria, which is absolutely vital for our economies”.