A passenger onboard the Boeing 777-300ER told The Associated Press that it appeared that someone on the flight set as many as five separate fires in different toilets over the course of the journey from Melbourne to the Emirati capital Abu Dhabi the previous day.
"A couple of hours into the flight it started to smell like smoke," said Caroline Martens, 27, a professional golfer from Norway who was on the flight.
"You could definitely tell the staff knew more than we knew. ... We understood there had been some sort of fire or cigarette smoking," she said.
Etihad said 254 passengers and crew were onboard when smoke was detected in two toilets, prompting the initial diversion to Indonesia.
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Once on the ground, the plane, passengers and carry-on luggage were searched, and passenger movement was restricted on the captain's orders, according to the carrier. Martens said lighters and matches were confiscated before passengers were let back on the flight.
Gatot Priambodo, the coordinator at Jakarta's Sukarno-Hatta International Airport, said Australian air traffic controllers requested the diversion after smoke alarms went off as the plane was cruising at 34,000 feet.
Ground crew said burned tissue paper in at least one of the toilets appeared to be the source of the smoke, he said. The flight then departed again to its scheduled destination of Abu Dhabi. Two hours before arrival, another smoke alarm sounded.
The smoke was "dealt with immediately by the crew," and the captain directed crew members to be stationed at each of the toilets to secure them for the rest of the flight, according to the airline.
"I freaked out when I looked at the map and we were in the middle of nowhere. We were over the ocean. ... That's when we realised this could actually end badly. It's not a joke anymore," she said.
Local authorities interviewed passengers and crew upon arrival, and the events on the flight are under investigation, the airline said.
No injuries were reported and no arrests have yet been made, the carrier confirmed. Officials at the Abu Dhabi police department, which is handling the investigation, could not be reached for comment.
The Boeing 777-300ER is a longer, extended-range version of the twin-engine 777 wide-body jet. Etihad has 10 of the planes in its relatively young fleet, according to its website.
Australia is an increasingly important market for Etihad. The government-backed carrier flies to Brisbane, Melbourne and Sydney, and in 2012 began buying a minority stake in Virgin Australia.