Passengers at airports in Spain, Portugal, France, Italy and Belgium are being forced to stand in immigration lines for "up to four hours", according to lobby group Airlines for Europe (A4E).
Mr Reynaert told the Times that delays had increased by 300%, compared to 2016, and that European Union members "must take the responsibility for this". "Queuing for up to four hours has been the top record these days", he said.
The checks affect people entering and leaving the Schengen area, which allows passport free movement through much of the EU.
It came as Ryanair, Europe's busiest airline, admitted that nearly a quarter of its flights had run late over a 24-hour period this week because passengers could not get through security to board flights to the UK.
"While border arrangements for Schengen countries are not in the United Kingdom government's control, I will be speaking to my counterparts in Portugal, Spain and Italy to urge them to do all they can to reduce queues and allow travellers to get on with their holidays".
This has taken up to two minutes per passenger which has led to delays.
The problems are set to continue throughout the summer holiday season, delaying tourists travelling in and out of popular destination airports including Madrid, Palma de Mallorca, Lisbon, Lyon, Paris-Orly, Milan and Brussels.
The Association of British Travel Agents said that it was "aware that new, stricter passport checks are resulting in longer queues at some airports".
People are being warned to check what terminal they are flying from, arrive in plenty of time for their flights and to expect large crowds in the airport.
"We have also hired additional security staff this year to help cope with growing passenger numbers".
At the same time, the European Commission has defended the increased security checks and reminded critics that this is all about protecting passengers and a direct response to requests from EU member states for more stringent checks. All EU member states wanted the current rules. "We can not have on the one hand a joint request from member states to have more checks and controls, to increase security, and the same time have complaints about longer waiting periods".
"We will be busy this weekend but are not experiencing heavy congestion.and we will have the extra customer care staff in place", a spokesman for the DAA said.
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