The fate of the passenger jet, which is presumed to have crashed at sea after disappearing en route from Kuala Lumpur to Beijing with 239 passengers and crew on board in March 2014, remains a mystery.
Five other fragments have previously been found and identified as definitely or probably from the Boeing 777.
All of them were discovered thousands of kilometres from the current underwater search zone far off Western Australia's coast, where three ships carrying sophisticated equipment are scouring the sea floor for traces of the plane.
"The Malaysian government is yet to take custody of the items, however as with previous items, Malaysian officials are arranging collection and it is expected the items will be brought to Australia for examination. These items of debris are of interest and will be examined by experts," Chester said in a statement. No other details were given.
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The first concrete evidence that MH370 might have met a tragic end was when a two-metre-long wing part known as a flaperon washed up on a beach on the French overseas territory of La Reunion in July last year.
In mid-May, the government agency leading the search for MH370, the Australian Transport Safety Bureau (ATSB), said two fragments that washed up on beaches in South Africa and Mauritius in March were also likely to have come from the jet.
One part, which came ashore at Mossel Bay in South Africa, was an aircraft engine cowling, identified from a partial Rolls Royce stencil. The other, which was found on Rodrigues island in Mauritius, was a decorative laminate from a "work table" in the main cabin.
If nothing turns up once the area is fully scoured, the search is likely to be abandoned, Australia, Malaysia and China - the countries that most of the passengers came from - have jointly said.