The Boeing 777-200 disappeared March 8 on a flight from Kuala Lumpur, the capital of Malaysia, to Beijing, China, with 239 people on aboard.
Australian authorities on Wednesday said satellite images showed what looked to be wreckage from the plane in the Indian Ocean, but that debris hadn't been found. Still, Abbott said he's optimistic.
"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," he said.
Australian search teams are taking charge of the search along the southern arc of where Malaysian authorities think the plane may have headed.
The Australians have put more aircraft into the search effort.
"Obviously, the more aircraft we have, the more ships we have, the more confident we are of recovering whatever material is down there," Abbott said. "And obviously before we can be too specific about what it might be, we do actually need to recover some of this material."