Issues have hit London's Gatwick and Heathrow airports, Charles de Gaulle in Paris and other locations including Washington DC, Melbourne and Singapore.
The check-in systems of affected airlines at Changi Airport have been restored after experiencing nearly three hours of technical glitch.
Failures of such systems, which are crucial to the operation of both an airline and an airport, have hit carriers in the past.
Singapore Airlines replied to Mr Concistre on Twitter, saying: "Hi Luis, please bear with us while our IT team is looking into the issue".
The problems were traced back to one software vendor, Amadeus, and its Amadeus Altea check-in software.
Carriers including British Airways, Deutsche Lufthansa, Cathay Pacific Airways and Qantas Airways were among those impacted, with Dutch operator KLM delaying at least 24 departures.
Airlines worldwide were forced to delay flights Thursday as a global flight-bookings system operated by Amadeus IT Group suffered what the company called a "network issue".
Gatwick and Heathrow have confirmed there are problems in several of their terminals.
Passengers trying to check-in for flights at Heathrow and Gatwick have been beset by delays caused by faulty software. "That action is ongoing with services gradually being restored", a company spokesperson told FOX Business in a statement.
Amadeus would not say how many airlines or airports were affected though reports cited airports around Europe and parts of the United States as being affected.