
The broad Topix gauge leapt as much as 1.3% to an unprecedented 3,146.58. The Nikkei 225 index of blue chip shares gained 1.45% to 43,643.81, near its own record. The yen softened 0.4% to 148 versus the U.S. dollar.
Japanese government bonds (JGBs) were resilient at first before falling late in the afternoon session, driving yields higher. The 20-year yield rose 3.5 basis points to 2.67%, while the 30-year yield jumped 6 basis points to 3.285%, matching the all-time high hit last week.
Yields on long-dated JGBs have surged of late due to global concerns about fiscal deficits and as pressure mounted on Ishiba from within his Liberal Democratic Party (LDP), while the Nikkei recently slipped from last month's all-time high.
Among top contenders in the LDP leadership race is Sanae Takaichi, a devotee of "Abenomics" policies of Shinzo Abe - Japan's long-time leader and former PM, who presided over massive stimulus and unprecedented monetary easing.
"Sanae Takaichi, who is considered to have a strong expansionary fiscal bias, could be perceived as more positive for Japanese equities," Morgan Stanley and MUFG Securities analysts, including Takeshi Yamaguchi, wrote.
"The risk of her favouring excessively dovish monetary policy appears lower than last year."
Meanwhile, Takaichi has largely been seen as bad news for Japan's already stressed bond market.
"She's known to favour stimulus measures and is viewed as wanting the Bank of Japan (BOJ) to take a cautious stance on policy, so that wouldn't be a great outcome for bond markets," Skye Masters, head of markets research at National Australia Bank, said in a podcast.
Money markets now show about a 20% chance the BOJ will hike its key interest rate by the end of October, down from 46% odds a week ago.
There were 197 advancers on the Nikkei index against 26 decliners. The largest gainers were chip designer Socionext , up 8%, followed by Mazda Motor Corp, which jumped 7.2%.
Mitsubishi Heavy Industries, which stands to gain from any increase in defence spending, surged 3.3%.
Advantest and SoftBank Group, two of the biggest beneficiaries of artificial intelligence (AI) investment in Japan, jumped 4.4% and 2.1%, respectively.
Ishiba's relatively conservative fiscal stance has been seen as a positive for the JGB market, where yields are relatively low globally, though Japan's massive debt pile and widening fiscal deficits continue to raise concerns.
The country's outstanding debt stands at nearly 250% of its gross domestic product (GDP), the highest among developed economies. Budget requests for the next fiscal year hit a record for the third straight year, the finance ministry said last week.
The JGB market was dealt a blow in mid July, when Ishiba's coalition suffered a considerable defeat in upper house polls. Outsider parties, campaigning on tax cuts and increased spending, gained seats, and speculation swirled for weeks about pressure on Ishiba to step down.
That all came to a head on Sunday, with Ishiba saying he must take responsibility for election losses and instructing the LDP to hold an emergency leadership vote.
The Nikkei share index hit a record high of 43,876.42 on August 19, riding a wave of optimism for corporate governance reforms and investment in AI.
Analysts in a Reuters poll see the index easing off that level to 42,000 by year-end.
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