Investors were also digesting weak US jobs data, while crude prices climbed after eight key members of the OPEC+ alliance said they had agreed to again boost oil production.
Tokyo's Nikkei index closed up 1.5 percent, with Japanese exporters benefiting from a slide in the yen's value -- one dollar bought 147.82 yen in afternoon trading, up from 147.07 on Friday.
Japanese bond yields also climbed after Ishiba said Sunday he would step down after less than a year in power, heralding fresh uncertainty for the world's fourth-largest economy.
"I don't think we can say that the resignation of PM Ishiba is a complete surprise as it's been mooted for some time but the timing of the announcement is certainly unexpected," said Michael Brown, senior research strategist at Pepperstone.
"As for the market reaction, this obviously introduces significant downside risks for the (Japanese yen) and for long-end" Japanese government bonds (JGBs), he added.
Last week, the yield on 30-year JGBs hit a record high, following rises in the United States and Europe on the back of concerns about political uncertainty and public finances.
Potential candidates to lead Japan's ruling party are "all likely to propose looser fiscal stances than Ishiba, hence further pressuring the long end of the curve, where demand for JGBs had already been waning quite significantly", Brown said.
Shanghai closed 0.4 percent higher. Hong Kong was up 0.8 percent, Taipei gained 0.2 percent and Seoul rose 0.5 percent.
Jakarta gained 0.6 percent and Wellington rose 0.4 percent, but Bangkok and Singapore were flat and Sydney shed 0.2 percent.
Last week's US jobs data has cemented expectations of a Federal Reserve interest rate cut later this month.
In Asia, "rising expectations of Fed rate cuts and with that lower US yields should be a welcome development to some extent providing some breathing space and policy room for Asian central banks", Michael Wan, senior currency analyst at Japanese bank MUFG, said in a note.
"Nonetheless, the key risk for Asian currencies would also lie in a sharp US slowdown and hard-landing recession through sharply slower exports to the US, which we stress is not our base case."
In early European trade, London was up 0.2 percent, Paris climbed 0.5 percent and Frankfurt jumped 0.7 percent.
- Key figures at around 0700 GMT -
Tokyo - Nikkei 225: UP 1.5 percent at 43,643.81 (close)
Hong Kong - Hang Seng Index: UP 0.8 percent at 25,618.79
Shanghai - Composite: UP 0.4 percent at 3,826.84 (close)
London - FTSE 100: UP 0.2 percent at 9,223.02
Euro/dollar: FLAT from Friday at $1.1722
Pound/dollar: UP at $1.3512 from $1.3508 on Friday
Dollar/yen: UP at 147.82 yen from 147.07 yen
Euro/pound: DOWN at 86.75 pence from 86.77 pence
West Texas Intermediate: UP 1.9 percent at $63.03 per barrel
Brent North Sea Crude: UP 1.9 percent at $66.72 per barrel
New York - Dow: DOWN 0.5 percent at 45,400.86 (close)
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