The Malaysia Airlines plane disappeared en route from Kuala Lumpur to Beijing on March 8, 2014 with 239 people on board. No trace has been found despite a massive surface and underwater hunt.
"I do reassure the families of our hope and expectation that the ongoing search will succeed," Abbott told parliament in Canberra.
"I can't promise that the search will go on at this intensity forever but we will continue our very best efforts to resolve this mystery and provide some answers."
The vessels are focusing on a 23,000 square mile priority zone, with the hunt scheduled to end in May. More than 26,000 square kilometres, or 40 per cent, of the ocean floor has been explored to date.
The intensive search -- jointly funded by Australia and Malaysia with a budget of AUD 120 million (USD 93 million) -- has so far only turned up a few shipping containers.
The ships, Fugro Supporter, Fugro Equator, Fugro Discovery and GO Phoenix, are working in one of the world's most isolated locations in treacherous conditions similar to the "Roaring Forties" north of Antarctica -- notorious among mariners for its hostile seas.
The agency coordinating the search, the Australian Transport Safety Bureau, has previously said a decision on continuing after the current hunt was completed was up to the Australian and Malaysian governments.
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