Passengers said there was shaking and "weird noises" after the plane suffered engine issues and was turned back to Auckland.
TAIC has now opened inquiries into both incidents, with investigators on the ground in Auckland since Tuesday.
TAIC chief commissioner Jane Meares said they needed to know the circumstances and causes of the events, and make any recommendations to stop them happening again.
"Our investigation team is working closely with the airline, Civil Aviation Authority, engine-manufacturer Rolls Royce, and our colleague agencies in the UK and USA.
"This is standard practice and in accordance with the international conventions covering aviation occurrence safety investigations.
"Our investigation team is securing and reviewing aircraft records including recorder information, making preliminary examinations of the engines, and interviewing company representatives and the flight crew."
Meares said they were satisfied that the company was doing the right things to ensure the travelling public's continuing safety.
She added that if the Commission felt that changes at any time, then it could issue urgent recommendations while inquiries continued.
Meares said that she couldn't make any further comment while the inquiry was underway.