On Wednesday, Air New Zealand's Auckland-Buenos Aires service was two hours enroute to Argentina when it turned back to Auckland after the crew was "alerted to abnormal indications on one of the engines", the TAIC said on its website.
Two flights were forced to return to Auckland this week after mechanical trouble, local media reported.
A company spokesperson said the Boeing 787-9 Dreamliner had returned as a precaution due to "a possible engineering issue".
In a statement to the New Zealand stock exchange on Thursday, Air New Zealand said as a result of recent Rolls Royce "engine events" on its Boeing 787-9 fleet, it would cancel and delay flights each day over the coming weeks.
Rolls-Royce said in August that components on some Trent 1000 engines were wearing out earlier than expected, according to reports.
Besiktas becomes first Turkish team to qualify for Champions League last 16
It is the only Turkish team to qualify from the group stage undefeated and advanced as the group leader. In the 87th minute, however, Leipzig's Naby Keita scored the equaliser to level the scoreline.
Japan's ANA and Britain's Virgin Atlantic have previously reported problems with the Trent 1000 engines.
An investigation is underway after two Air New Zealand 787 aircraft experienced engine abnormalities in recent days.
Air New Zealand chief operations integrity and standards officer David Morgan told the NZ Herald the the blades failed on the flight to Tokyo Narita, while exhaust gas temperature rises indicated problems with the engine.
The country's national carrier said the engines on the 787-9 fleet require maintenance "sooner than previously advised".
"Our investigation team is working closely with the airline, Civil Aviation Authority, engine-manufacturer Rolls Royce, and our colleague agencies in the United Kingdom and USA".
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