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The 10-metre ferry reported that it was in trouble on January 22 amid monsoon warnings near Alcester Island in the Solomon Sea, about 1000 kilometres northeast of Cairns.
The Australian Maritime Safety Authority sent out its Queensland-based Challenger jet to search for the missing vessel across some 6000 square kilometres.
AMSA also asked ships in the area to search for the boat and its crew, response centre manager Stephen Hart said on Monday.
Showers and thunderstorms hampered search efforts, with widespread rain reducing visibility.
A cargo ship named Ken Hope found the missing boat on January 29 and rescued the 13 people aboard.
All the survivors were in good health and taken to Misima Island, about 300km south of where the vessel was reported broken down.