Under the EES system, digital records linked to passports track when “third country” nationals – including British and American travellers – enter and leave the so-called Schengen free movement zone, which includes 29 European countries.
However, Airlines UK and Airlines for America said the EES rollout had been inconsistent.
They added “with peak summer travel approaching and the system not yet working as it should, airlines need the commission and member states to get serious about contingency measures and take a pragmatic look at whether the current timeline is realistic”.
Steve Heapy, chief executive of Jet2, said his airline found “the continued pursuit of a policy so baffling – in cases where it has clearly not been implemented in a robust manner”.
He said allowing EES checks to be paused where systems were not ready would “result in a much better experience for holidaymakers”.
Von Massenbach said there had been a “very high level meeting in Brussels” on Wednesday, “and we see now that they start to understand that this is a situation that is not bearable, not bearable over the summer”.
Airports lobby group, ACI Europe, have written to EC president Ursula Von Der Leyen, claiming wait times at border control had now reached up to five hours in peak traffic periods, and things could worsen as the busiest time of the year approached.
It warned “airlines face half-empty planes at gate closing time, while passengers are stuck in border control queues”.
Countries do have the ability to suspend EES checks under some circumstances.
However, ACI Europe argued states needed to be allowed to pro-actively suspend the system if high volumes of passengers are expected.
An EC spokesman said that “all efforts are being made to limit the impact [of EES] on travellers from outside the EU”.
He said the impact was “limited” in “most” EU airports and where there were issues, member states had not been able to provide sufficient numbers of border guards, appropriate infrastructure and automated equipment.
He said the EC continued to offer support with the new system, and was willing to do even more “in view of the coming summer period”.
