Abbott told parliament "new and credible information" had come to light nearly two weeks after the plane vanished.
He said an Australian air force Orion had already been diverted to look into the objects with three more surveillance planes to follow. He did not specify where they were but Australia has taken charge of the search in the southern Indian Ocean.
"The Australian Maritime Safety Authority (AMSA) has received information based on satellite information of objects possibly related to the search," Abbott said, adding that he had informed Malaysian Prime Minister Najib Razak.
"Following specialist analysis of this satellite imagery, two possible objects related to the search have been identified."
But he warned against drawing any premature conclusions.
"We must keep in mind the task of locating these objects will be extremely difficult and it may turn out that they are not related to the search for flight MH370," he said.
AMSA was due to hold a news conference with more details at 0430 GMT.
Authorities in Kuala Lumpur on Monday asked Canberra to take responsibility for the "southern vector" of the operation to locate the Boeing 777, which disappeared on March 8 en route to Beijing with 239 passengers and crew on board.
The Malaysian government believes the jet was deliberately diverted and flew for several hours after leaving its scheduled flight path -- either north towards Central Asia, or towards the southern Indian Ocean.
Australian, US and New Zealand long-range surveillance planes have been scouring a vast tract of the southern Indian Ocean since Tuesday with the search focused on an area of 305,000 square kilometres (122,000 square miles), some 2,600 kilometres southeast of Perth.