"We have narrowed down the search area and we are very confident that the signals that we are detecting are from the black box of the MH370," Abbott said.
Australian Defence Vessel (ADV) Ocean Shield detected four signals Saturday and Sunday, Xinhua reported.
The last signal was picked up by an Australian surveillance plane Thursday.
"We are hoping to get as much information as we can before the signal expires," he added.
The search area is narrowed down from 75,000 square km to 57,923 km
The Joint Agency Coordination Center (JACC) of Australia, which is heading the international search effort, however, said in a statement Friday that the signal picked up by an Australian surveillance plane Thursday was not related to the missing flight after analysis.
A Royal Australian Air Force (RAAF) AP-3C Orion aircraft detected a suspicious signal Thursday in the vicinity of the ADV Ocean Shield.
Up to 14 planes and 13 ships joined in Thursday's search for the Malaysia Airlines flight MH370, missing since March 8.
"The Australian Joint Acoustic Analysis Centre has analysed the acoustic data and confirmed that the signal reported in the vicinity of the ADV Ocean Shield is unlikely to be related to the aircraft's black box," said JACC chief Angus Houston.
According to JACC figures, the ADV Ocean Shield is narrowing down the search area from 75,000 square km to 57,923 km, which lies approximately 2,280 km northwest of Perth.
Except for the search operation on the ocean surface, the underwater search also continues, with the Ocean Shield at the northern end of the defined search area, and Chinese ships Haixun 01 and HMS Echo at the southern end.
Two separate signals were detected Sunday by a US pinger locator being towed by the ADV Ocean Shield in the Indian Ocean search area, about 1,700 km northwest of Perth.
The first detection of the signal lasted for two hours and 20 minutes. After a few hours, the second signal was detected which lasted for 13 minutes.
The two signals were about 1800 metres apart.
The ADV Ocean Shield detection Sunday came shortly after a Chinese patrol vessel, the Haixun One Zero, reported detecting two pulse signals Friday night, and then again Saturday at a frequency consistent with black box technology.
The Malaysia Airlines flight MH370 vanished mysteriously about an hour after taking off for Beijing from Kuala Lumpur shortly after midnight March 8.
The Boeing 777-200ER was scheduled to land in Beijing the same day. The 227 passengers on board included five Indians, 154 Chinese and 38 Malaysians.