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Australian authorities deeply regret not finding missing Malaysia Airlines flight MH370 and describe the protracted mystery as "unacceptable" in a final report, published Tuesday, on the unsuccessful search.

"The reasons for the loss of MH370 cannot be established with certainty until the aircraft is found," the Australian Transport Safety Bureau (ATSB) said in the report.

"It is almost inconceivable and certainly societally unacceptable in the modern aviation era ... for a large commercial aircraft to be missing and for the world not to know with certainty what became of the aircraft and those on board."

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The disappearance of the Boeing 777 on March 8, 2014, with 239 people on board, on a flight to Beijing from the Malaysian capital of Kuala Lumpur, has become one of the world's greatest aviation mysteries.

It is thought to have been diverted thousands of miles off course out over the southern Indian Ocean before crashing off the coast of Western Australia.

Australia, which led the underwater hunt, and Malaysia and China called off a $160 million search for the plane in January after finding nothing, despite the protests of families of those onboard.

Australia's main scientific agency said in August it believes with "unprecedented precision and certainty" that the plane crashed northeast of the search zone. But those findings were dismissed by Australia's government at the time as not specific enough, and the search has not been re-opened. Doing so depends on finding credible, new evidence about the plane's whereabouts.

The ATSB report published Tuesday detailed the fruitless 1,046-day hunt for the plane, above and below the surface of the Indian Ocean, and scientific analyses of satellite pictures, sea currents and even barnacles found clinging to a piece of the plane found on Reunion Island.

"The understanding of where MH370 may be located is better now than it has ever been. The underwater search has eliminated most of the high probability areas," the ATSB said.

"We...deeply regret that we have not been able to locate the aircraft, nor those 239 souls on board that remain missing."

It recommends aircraft and aircraft equipment manufacturers investigate providing better methods of automated satellite tracking for planes if they encounter problems during flight in future.

Malaysia has continued to investigate the plane's whereabouts and in August said it received an offer from a private seabed exploration firm, Ocean Infinity, to resume the search.