The engine issues both happened on Boeing 787 Dreamliner planes flying out of Auckland bound for worldwide destinations.
And on Tuesday, the airline's flight to Tokyo Narita also returned to Auckland due to what the TAIC again said were "abnormal indications on one of the engines".
Last night another Air New Zealand 787, headed to Buenos Aires, Argentina, experienced an engine issue shortly after leaving Auckland and was also forced to return.
Auckland Airport has welcomed the announcement by Air New Zealand and Singapore Airlines that they will increase flights on the Singapore to Auckland route.
Tan Kai Ping, Singapore Airlines' senior vice president, marketing planning, said: "Our alliance with Air New Zealand has already benefited customers through more capacity, choice, improved connections and more codeshare destinations".
New Zealand's Transport Accident Investigation Commission says on its website that it is investigating two "engine abnormality" incidents involving Air NZ 787-9s that occurred on 5 and 6 December.
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Customers are encouraged to check this first before calling the airline's contact centre.
Rolls-Royce says that it regrets the disruption caused to Air NZ, and the two parties are working together to restore full operations of the Trent 1000 engines as soon as possible.
During peak months the airlines will jointly operate a total of 35 return services a week between Singapore and New Zealand, including Christchurch and Wellington flights.
The company has said previously it expect to an improvement in earnings in the current financial year, compared with the 2016/17 result.
The Air New Zealand incidents have been reported worldwide, including on the BBC and by global agency Reuters.
"It's not uncommon for long-term engine programmes to experience technical issues during their life and we manage them through proactive maintenance", it adds.