The Morrison government privately hopes Shinzo Abe's successor doesn't soften its stance on key security alliances and lean more towards China.
The Japanese Prime Minister has been battling a chronic illness.
Shinzo Abe,who turns 66 next month,reached a milestone as the PM with the most consecutive days in office on Monday,fuelling speculation he may resign.
Japan suffered its biggest economic contraction on record in the second quarter as the coronavirus pandemic crushed business and consumer spending.
The two leaders talked up the importance of having Taiwan as an observer at the World Health Assembly,months after China successfully blocked the island nation from participating in the forum.
Australia and Japan will form a space agreement,while the two countries also look to deepen their defence and security ties in the face of a rising China.
The Japanese government has repeatedly expressed deep concern about China's plan to enact sweeping national security legislation in the former British colony.
Virtually every country has broken the EU's deficit limit while spending to keep health care systems,businesses and jobs alive.
Japan is on course for its deepest postwar slump as the coronavirus crisis takes a heavy toll on businesses and consumers
The number of cases in Singapore has more than doubled over the past week largely due to an explosion in infections among foreign workers.
Japanese Prime Minister Shinzo Abe on Tuesday declared a state of emergency to fight new coronavirus infections in major population centers and unveiled a stimulus package he described as among the world's biggest to soften the economic blow.