A day after raising hopes of a breakthrough and expressing confidence that signals from the black box on Malaysia Airlines flight 370 had been traced, Australian Prime Minister Tony Abbott cautioned that finding the missing Boeing 777 still remained “a massive task.”

“No one should underestimate the difficulties of the task that still ahead of us,” he said as he concluded a visit to China.

Signals that were detected in the remote waters of the southern Indian Ocean were “rapidly fading,” he said. Batteries on the black box, which records vital flight data, usually last for 30 days; the aircraft disappeared early on March 8.

“Trying to locate anything 4,500 metres beneath the surface of the ocean, about a 1,000 km from land is a massive, massive task,” he said.

The search area on Saturday had been further narrowed to a grid 40 km by 50 km, Mr. Abbott said.

In a meeting with President Xi Jinping, the Australian Prime Minister thanked China as “the very first country to provide ships for the search.”

On board the aircraft were 239 people, including 154 Chinese nationals, 38 Malaysians and 5 Indians.

Mr. Xi “expressed gratitude” for Australia’s leading role in the search efforts in the Indian Ocean and said China would continue deploying resources to scour the remote waters.

Malaysian media reports on Saturday said co-pilot Fariq Abdul Hamid may have attempted to make a call from his mobile phone shortly after the Beijing-bound plane had diverted from its flight path and headed west, around an hour after taking off from Kuala Lumpur.

Quoting unnamed investigators, the New Straits Times reported that the call, made somewhere near Penang, close to the aircraft’s last point of contact, “ended abruptly, but not before contact was established with a telecommunications sub-station in the state.”

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