Australian vessels have been searching in the southern Indian Ocean for the aircraft, which disappeared on 8 March with 239 people on board.
Abbott said the objects had been identified on satellite imagery.
An Orion aircraft had been sent to the area to try to locate the objects, Mr Abbott told parliament.
Malaysia Airlines flight MH370 was flying from Kuala Lumpur to Beijing when it lost contact with air traffic controllers.
Twenty-six nations have been involved in a major search for the missing plane, which Malaysia says was intentionally diverted.
Investigators have been scrutinising the backgrounds of both the crew and the passengers, but have so far identified no evidence of terror or other potentially relevant links.
Southern corridor
"The Australian Maritime Safety Authority has received information based on satellite information of objects possibly related to the search," Abbott said.
"Following specialist analysis of this satellite imagery, two possible objects related to the search have been identified."
Three more aircraft would follow the Orion to the search area, he added.
Abbott warned, however, that finding the objects would be very difficult and said they could turn out to be unrelated to the Malaysian aircraft.
A number of sightings of possible debris have been investigated in the search for the plane but so far none have proved to be linked.
Earlier this week, Australia was asked by Malaysia to take responsibility for the "southern corridor" search.
Investigators had identified two corridors of territory - one to the north and one to the south - spanning the possible positions of the plane about seven hours after take-off.
This was based on its last faint signal to a satellite - an hourly "handshake'' broadcast even when the main communication systems are switched off.
The plane lost contact with controllers over the South China Sea as it crossed from Malaysian to Vietnamese air space.
Malaysian officials say it then turned west and its last position - according to Malaysian military radar - was over the Malacca Straits, in the opposite direction to its planned flight path.
Attention has focused on the crew and on Wednesday multiple unidentified US officials said that the FBI was helping Malaysia analyse data from a flight simulator taken from the captain's home.
Malaysia's Acting Transport Minister Hishammuddin Hussein, at a press conference on Wednesday, stressed the captain should be considered innocent until proved otherwise and said that members of his family were co-operating with the investigation.
(BBC)