"It's still too early to be definite, but obviously we have now had a number of very credible leads and there is increasing hope -- no more than hope, no more than hope -- that we might be on the road to discovering what did happen to this ill-fated aircraft," Abbott said.
The prime minister spoke after several unidentified objects were seen in the search zone for the Boeing 777, about 2,500 kilometres off Perth.
The comments came hours after the Australian Maritime Safety Authority (AMSA) announced that "further attempts will be made to establish whether the objects sighted are related to MH370," on Sunday.
The prime minister did not specifically mention a Chinese satellite image dated March 18 and released yesterday, which showed a large piece of floating debris close to where previous satellite images showed two pieces of possible wreckage in the remote ocean.
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Abbott's confidence was also supported, he said, by the growing resources being thrown at the hunt.
"Obviously the more aircraft we have, the more ships we have, the more confident we are of recovering whatever material is down there," he said.
"And obviously before we can be too specific about what it might be, we do actually need to recover some of this material."
Abbott, speaking as he ended a visit to neighbouring Papua New Guinea, praised the international search effort.
"I want to say that this is a really big international effort and it does show that many countries are capable of pulling together in a time of trouble.
MH370 dropped off civilian radar on March 8 en route from Kuala Lumpur to Beijing, and two weeks later Malaysian investigators still believe it was deliberately diverted by someone on board.