All 40 passengers disembarked on the runway after the plane arriving from Christchurch landed trailing smoke and fire.
Dramatic video posted on social media showed the plane arriving with smoke billowing behind it, and one passenger told RNZ "people were scrambling, terrified".
TAIC has launched an investigation into the cause of the engine fire.
A team of investigators were examining the plane, extracting electronic and hard copy data, and interviewing the crew on Monday and Tuesday, senior communications advisor Simon Pleasants said.
TAIC also wanted to hear from anyone who saw anything, including passengers - especially if they had video footage, he said.
"Getting the facts straight is really vital."
It would be some time before the cause of the fire was understood, as aviation inquiries currently took an average of 18 months to two years to complete. It was unlikely the plane would be impounded, but investigators may remove items that could be later examined at TAIC's technical facility in Wellington, or sent overseas, he said.
Mary Longmore was travelling on the plane with her daughter, and said it was "incredibly scary" seeing sparks, then a lot of smoke, then flames coming out of the engine.
She said she told the steward the engine was on fire, and he called the captain.
"They hadn't said anything to us probably because they didn't want to panic people. Clearly the steward didn't know because I saw their faces when I told them that the engine was on fire."
Longmore believed she and her daughter were the first to see the flames.
"We were sitting literally right next to it, so the flames were just a few inches away outside the window, shooting out in a jet. It was smoke in the cabin, and you could smell it, it was quite acrid and then they said 'evacuate'."
Video showed passengers jumping from the emergency doors.
Anyone who saw what happened or has pictures or videos should email info@taic.org.nz.
