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On Sunday night, Australia's Prime Minister Scott Morrison became the first foreign leader to speak with Yoshihide Suga, congratulating him on his appointment.
Mr Morrison conveyed his appreciation for the Japanese coastguard search for Gulf Livestock 1, which sank on September 2 after Typhoon Maysak struck at sea.
Mr Suga said the search was continuing and Japan would co-operate as much as possible.
Two Australians - Queensland vet Lukas Orda and NSW man Will Mainprize - are missing, as well as 36 Filipinos and two New Zealanders.
Of the ship's 43 crew, three were rescued - all Filipinos - but one later died after being found unconscious.
Mr Morrison and Mr Suga also discussed economic and security issues, including North Korean abductions and support for Pacific island nations.