The Nikkei 225 ended up 0.70% at 16,519.29 and the Topix closed up 0.80% at 1,311.50. Japanese stocks had risen on Friday after five days of losses amid nervousness about the Bank of Japan's policy meeting on Wednesday. Banking stocks had been particularly hard hit, on expectations the central bank would push its deposit rate further into negative territory.
On Monday Sumitomo Mitsui Trust closed up 5.6%.
Mitsubishi UFJ Financial closed up 2.7% and Sumitomo Mitsui Financial gained 2.4%.
Apple supplier Alps Electric led the Nikkei 225 higher, gaining 6.3% on analysts' commentary about strong sales of the new iPhone 7 and the costlier 7-Plus, which have been aided by the recall of Samsung's Galaxy Note 7. On Thursday Apple said initial 7-Plus supplies have sold out, along with those of jet black iPhone 7 models, and that the devices won't initially be available for walk-in customers at Apple stores.
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Taiwanese chip maker Hon Hai Precision Industry (HNHPF) closed up 3.9%, while Advanced Semiconductor Engineering was up 3.3% in Taipei.
Australian legal firm Slater & Gordon edged 0.6% higher during a chopping Sydney session during which trading had to be halted because of technical problems at the Australian Securities Exchange.
Slater & Gordon said it would sue the U.K.'s Watchstone over last year's £673 million ($878 million) acquisition of the U.K group's professional services division , which triggered steep write-downs and a restructuring of its debt.
U.S. futures were up, with the Dow Jones mini gaining 0.42% and the S&P 500 mini up 0.40%.
In Hong Kong the Hang Seng was up 0.91% at 23,549.07.
On mainland China the CSI 300 was up 0.60% at 3,258.42.
Oil rose, with West Texas intermediate recently up 1.74% at $43.78 a barrel. The commodity gained on shipment problems at Libya's ports and a Sunday tweet from Venezuelan President Nicolas Maduro claiming OPEC will reach an output cap at a meeting in Algeria later this month.
In Sydney the S&P/ASX 200 was down 0.04% at 5,294.80.