Australian officials still expect to be sent the second potential piece of wreckage from MH370 for testing but are yet to receive any reports of a third item.
Two years after the Boeing 777 carrying 239 people disappeared, the third piece of debris was reportedly discovered on the shores of La Reunion, the Indian Ocean island where the first confirmed piece from the plane was found in July.
The third item was said to have been found by Johnny Begue, the same member of a beach clean-up crew who found the first object, a wing piece known as a flaperon.
An Australian Transport Safety Bureau spokesman told AAP on Sunday they had not received any reports of a third find.
He said the second possible piece of MH370 debris, which has the words "NO STEP" on it and was discovered on a sandbank in the Mozambique Channel last week, was still expected to be sent to Australia for testing.
But it could go to Malaysian authorities instead, with the likely involvement of manufacturer Boeing, he said.
After the discovery in Mozambique last week, the ATSB said the object was of interest because it had been found in an area where plotting had indicated debris from MH370 could have drifted.
Tuesday marks two years since the Malaysia Airlines jetliner disappeared en route from Kuala Lumpur to Beijing, killing 239 people, including six Australians.
It's believed it crashed somewhere in the southern Indian Ocean, off Western Australia.
Malaysian Transport Minister Liow Tiong Lai last week urged families of the passengers to file claims for damages against Malaysia Airlines by Tuesday.
There is a two-year cut-off for such claims under Article 35 of the 1999 Convention for the Unification of Certain Rules for International Carriage by Air, known as the Montreal Convention.
"The government of Malaysia remains ever conscious that the families and next-of-kin of the passengers and crew of MH370 need to be accorded their legitimate rights as provided under the relevant international instruments and domestic laws," the minister wrote.
Later on Sunday, the support group for family of passengers, Voice 370, will hold a public remembrance event at The Square in Publika, Kuala Lumpur, to mark two years since the plane vanished.
The group fears the search for wreckage will be abandoned completely if nothing significant is found in the current 120,000 square kilometre search area.
More than 85,000sq km of the seafloor has been combed so far and the remainder is expected to have been scoured by the middle of the year.
The governments of Malaysia, Australia and China - where most of the passengers came from - have agreed not to further expand the search area in the absence of credible new information.
"Voice 370 urges authorities to press on and search on in the current search area," the support group said in a statement last week.
"It should continue beyond 2016 because international aviation stands to benefit immensely from answers that the search would yield should debris be salvaged and studied, and lessons learnt would make aviation safer."
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