Abbott arrived at Perth's Royal Australian Air Force (RAAF) base Pearce this morning, even as the search continues to find the lost Malaysia Airlines flight MH370.
Speaking here Abbott said "We can keep searching for quite some time to come and we will keep searching for quite some time to come. I'm certainly not putting a time limit on it".
Appreciating the contribution of those who were involved in the search operation, Abbott said the "best brains in the world" are on the task but until any wreckage was found, authorities will have to keep relying on "guesstimates".
"All of the technological mastery that we have is being applied. So if this mystery is solvable, we will solve it," he said, adding "But I don't want to underestimate just how difficult it is".
Abbott said that it was "tremendous" to see such international cooperation. "We have regular military cooperation with the United States, with New Zealand and with Malaysia, but to see also the cooperation with us from China, from Japan and from Korea is really heartening," he said.
"It demonstrates that in a humanitarian cause, the nations of this region can come together to work for the betterment of humanity, can work to try to resolve this extraordinary mystery, can work to try to bring peace and closure to the families of the 239 people on board that ill-fated aircraft. Abbott said "It's only reasonable that we should bear this cost.
It's an act of international citizenship on Australia's part. At some point there might need to be a reckoning. "There might have to be some kind of tallying, but nevertheless we are happy to be as helpful as we can to all of the countries with a stake in this, and let's not forget it's not just Malaysia, there's China obviously which had the largest number of citizens on the aircraft," he said.
Abbott, according to media reports here, said retired Air Chief Marshal Angus Houston, country's former defence force chief, will lead a new joint agency co-ordination centre (JACC) in Perth to find the debris of the stricken jetliner.
"There is no one better placed than Angus to co-ordinate and liaise given the quite significant number of countries that all have a stake in this search," he said.