The New Straits Times of Malaysia in a front page exclusive report Monday, quoting members of the International Investigation Team (IIT) based in Kuala Lumpur, claimed they were thinking of starting right from the beginning to solve the case of MH370.
That the aircraft may have landed elsewhere than the southern Indian Ocean was under consideration, the report said.
Abbott said "under-sea searching" was being conducted at the moment within a circle with a radius of about 12 km, an area of just under 400 sq km.
He stressed that the search operation was still going on and would continue.
"We haven't finished the search. We haven't found anything yet in the area that we're searching, but the point I make is that Australia will not rest until we have done everything we humanly can to get to the bottom of this mystery."
He said "there is reasonable hope of finding something" while pledging Australia "will not let down the families of the 239 people who were on that plane by lightly surrendering".
While more than 80 percent of the focused underwater search area has been completed by Wednesday morning, Abbott said if at the end of that period nothing is found "we are not going to abandon the search".