The resignations of the two women could complicate tough decisions on key policies, including whether to go ahead with an unpopular plan to raise the national sales tax and planned restarts of nuclear reactors that were shut down after the 2011 Fukushima disaster.
               
Abe hopes to contain the damage with swift replacements, but the opposition is looking for other potentially vulnerable ministers also appointed in an early September cabinet reshuffle. Further resignations could raise doubts about Abe's own future, some political experts said.
               
Trade and Industry Minister Yuko Obuchi, 40, the daughter of a Prime Minister and tipped as a future contender to become Japan's first female premier, told a news conference she was resigning after allegations that her support groups misused political funds.
               
Just hours later, Justice Minister Midori Matsushima also resigned. The opposition Democratic Party had filed a criminal complaint against Matsushima, accusing her of violating the election law by distributing paper fans to voters.
               
Obuchi and Matsushima were two of five women appointed by Abe in the cabinet reshuffle less than two months ago - a move intended to boost his popularity and show his commitment to promoting women as part of his "Abenomics" strategy to revive the economy.
               
"I appointed them and as prime minister, I bear responsibility," Abe told reporters at his office.

"I deeply apologise to the people of the nation." Abe added he wanted to pick successors for the two posts within the day.
               
As head of the powerful Ministry of Economy, Trade and Industry (METI), Obuchi, a telegenic mother of two, was tasked with selling Abe's unpopular plan to restart nuclear reactors to a wary public worried about safety.
               
"We cannot let economic policy and energy policy stagnate at METI because of my problems, so I will resign my position," a solemn Obuchi told a nationally televised news conference, bowing deeply in apology.
               
The departures are the first cabinet resignations for Abe, who took office in December 2012 for a rare second term, promising to revive Japan's stalled economy and strengthen its security stance to cope with challenges such as a rising China.
              
Abe's first stint as Prime Minister in 2006-2007 was marred by scandals among his ministers - several quit and one committed suicide. Abe himself resigned after just one year in the face of parliamentary deadlock, sliding support rates and ill health.
               
His current government had been little touched by scandal until the cabinet rejig. Abe's ruling coalition has a hefty parliamentary majority and no general election need be held until 2016, but the opposition Democrats have taken aim at new ministers in debates to try to dent Abe's popularity.
               
Defence Minister Akinori Eto, also appointed in September, has faced questions from the opposition over his political funds.
               
"They are trying to limit the damage by getting rid of those (two) quickly," said Tomoaki Iwai, a political science professor at Nihon University.

"But Abe's support will decline and … policy implementation will not go smoothly," he said, adding the situation would become far tougher if other ministers also quit.
               
Abe must decide by year-end whether to implement a planned hike in the sales tax to 10 percent from October 2015, after a rise in April to 8 percent pushed the world's third-largest economy into its deepest quarterly slump since the 2009 global financial crisis.
               
Worries about his support rate - which has already begun to sag, could complicate Abe's decision on raising the levy.
               
"I think there is a big possibility that in order to prevent his support rates from falling, the sales tax rise could be delayed for a year and a mid-sized economic package crafted," said Koichi Kurose, chief economist at Risona Bank.
               
Abe's support fell 6.8 percentage points to 48.1 percent in a weekend survey by Kyodo news agency from last month. Nearly two-thirds opposed a second tax hike and almost 85 percent said they didn't feel the economy had recovered.
               
Abe had hoped the soft-spoken Obuchi would be able to ease opposition to atomic power. Some political analysts said the controversy could hamper Abe's plan to reboot reactors - opposed by more than 60 percent of voters in the Kyodo survey – but others said he was likely to stick to the policy.
               
The scandals could also dampen the outlook for legislation to legalise casino resorts, a move that Abe has said would help the economy by boosting tourists but which many voters oppose and about which Abe's coalition partner has doubts.
               
Media reports of Obuchi's funding irregularities emerged on Thursday. On Saturday, NHK said two Obuchi political groups spent 43 million yen (USD 400,000) on annual theatre events between 2009 and 2011 and kept no record of spending on the 2012 event.
               
Obuchi said on Monday that an examination of records had uncovered questionable outlays for the theatre events and she would ask outside accountants and lawyers to take a closer look. (1 US dollar = 107.1800 Japanese yen)

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