LONDON—Airlines are resisting early European Union plans that could push some of the costs and responsibility for implementing vaccination passports onto the industry.

The EU is moving ahead with plans to roll out a “Digital Green Certificate”—a document to store Covid-19 information such as vaccination records and test results. Governments, airports and airlines hope that will spur travel across the bloc by making it easier to check if passengers have been inoculated.

“Vaccines are what is going to ultimately allow us to start recovering as an industry,” said Olivier Jankovec, director general of Airports Council International Europe, a trade body of airports. “It’s what is going to allow Europeans to be mobile again.”

On Friday, the U.S. Centers for Disease Control and Prevention said people who are fully vaccinated against the new coronavirus can travel without serious risk, easing its blanket advice against travel.

The EU plan is still in flux, but governments are fast-tracking the project for a mid-June rollout. The basic concept: Europeans who are vaccinated will be issued a certificate, either paper or electronic, with a bar code that can be scanned at airports to verify vaccination.