The last vessel searching for missing MH370 has left on its final sweep across the southern Indian Ocean, Australia said Wednesday, as the transport minister cautioned the airliner might not be found in coming weeks.

Fugro Equator sailed from Fremantle port on Australia's western coast on Monday for the 120,000 square-kilometre (46,000-square-mile) zone where investigators believe the Malaysian Airlines jet disappeared en route from Kuala Lumpur to Beijing on March 8, 2014, carrying 239 passengers and crew.

No trace has been found in the massive undersea hunt off Australia but investigators have confirmed that three pieces of debris recovered on western Indian Ocean shorelines came from MH370.

"It has been an heroic undertaking but we have to prepare ourselves for the prospect that we may not find MH370 in the coming weeks, although we remain hopeful," Transport Minister Darren Chester told The West Australian Tuesday.

The newspaper added that the ship's final hunt would involve examining some 200 small areas which were either too deep for previous sweeps or were not properly examined due to poor sonar readings.

The government agency leading the search, the Australian Transport Safety Bureau (ATSB), said Wednesday that the Equator's mission was expected to draw to a close next month.

Many next-of-kin have repeatedly complained about the lack of a coordinated search in the western Indian Ocean and along the African coast.

Relatives of some of the missing passengers are currently in Madagascar, combing beaches for clues about the lost plane, after fragments identified with "near certainty" as coming from MH370 were discovered in recent months on the coast of East Africa.

The families have been accompanied by American amateur investigator, Blaine Gibson, a lawyer from Seattle who has travelled the world trying to solve the MH370 mystery.

Gibson has also recovered other possible MH370 debris, but authorities have yet to confirm if any of the pieces belong to the missing plane.

Neither the location nor the cause of the crash are known, feeding wild conspiracy theories.

The ATSB said in a report last month that MH370 was likely out of control when it plunged into the ocean with its wing flaps not prepared for landing. It cast doubt on theories a pilot was still in charge.

The governments of Australia, Malaysia and China, where most of the passengers were from, agreed to pull the plug on the operation once the search area was fully scoured unless "credible new information" emerged.