No trace of the Boeing 777 has been found nearly four weeks after it vanished in the early hours of March 8 on a flight from Kuala Lumpur to Beijing with 239 people on board.
Ten planes and nine ships were involved in search operations Thursday, scouring the ocean far off Australia's southwest corner where investigators believe the plane may have ended up after unknown events occurred on board.
Najib, whose government has been harshly criticized by some victims' families for giving sometimes conflicting information about the flight and for the slow pace of the investigation, said everyone involved in the search is thinking of the families of victims who are waiting desperately for news.
"I know that until we find the plane, many families cannot start to grieve," Najib said. "I cannot imagine what they are going through. But I can promise them that we will not give up.
"We want to provide comfort to the families and we will not rest until answers are indeed found. In due time, we will provide a closure for this event," he said.
Najib met with Abbott at the Australian base near Perth that is serving as the hub for the multinational search effort. They were briefed by Angus Houston, the head of a joint agency overseeing the search.
Although Australia is coordinating the ocean search, the investigation into the tragedy ultimately remains Malaysia's responsibility. Najib said Australia had agreed to be an "accredited representative in the investigation," and would work with Malaysia on a comprehensive agreement on the search.
On Wednesday, officials warned the investigation may never fully answer why the airliner disappeared. A dearth of information has plagued investigators from the moment the plane's transponders, which make the plane visible to commercial radar, were shut off.
Military radar picked up the jet just under an hour later, way off course on the other side of the Malay Peninsula. Authorities say that until then, its "movements were consistent with deliberate action by someone on the plane," but have not ruled out anything, including mechanical error.
Police are investigating the pilots and crew for any evidence suggesting they may have hijacked or sabotaged the plane. The backgrounds of the passengers have been checked by investigators and nothing suspicious has been found.
The search for the plane began over the Gulf of Thailand and South China Sea, where its last voice communications were, and then shifted west to the Strait of Malacca. Experts then analyzed hourly satellite "handshakes" between the plane and a satellite and now believe it crashed somewhere in the southern Indian Ocean.
Thursday's search zone was a 223,000-square kilometer (86,000-square mile) patch of ocean 1,680 kilometers (1,040 miles) northwest of Perth, part of a larger area crews have been scouring since last week.
The British navy's HMS Echo reported one alert as it searched for sonic transmissions from the missing plane's flight data recorder, but it was quickly discounted as a false alarm, the Joint Agency Coordination Center overseeing the search said Thursday.
False alerts can come from animals such as whales, or interference from shipping noise.
No confirmed trace of the plane's wreckage has been found. Houston has said there is no timeframe for ending the search, but acknowledged a new approach will eventually be needed if nothing turns up.