* Euro falls from 3-week high as bank worries rekindled
* Greenback near 15-yr low vs yen, BOJ takes no action
* Aussie down after RBA statement, Labor wins power
By Rika Otsuka
TOKYO, Sept 7 (Reuters) - The euro fell on Tuesday from a three-week peak against the dollar hit the previous day, as rekindled worries about the European banking sector prompted investors to cut risks.
The euro fell 0.6 percent on the day to $1.2797 after triggering stop-loss orders in the $1.2850-60 area, as a Wall Street Journal report stoked fears about the viability of European banks by highlighting the weakness of euro zone stress tests earlier in the year.
The single currency was further pressured as Germany's banking association said on Monday the country's 10 biggest banks may need 105 billion euros of additional capital under a revamp of banking rules designed to prevent future financial crises.
The euro on Monday rose as high as $1.2920, its highest in almost three weeks. It is now testing support at $1.2795-80, with the 21-day moving average at $1.2795 on Tuesday and the 55-day moving average at $1.2788.
"Concerns about euro zone banks have been growing again, hitting investor sentiment that had improved a little after better-than-expected U.S. jobs data last week," said Tsutomu Soma, senior manager of the foreign securities department at Okasan Securities.
"The trend in the euro might have changed as the market's mood is shifting back toward risk reduction."
The dollar index, a gauge of the U.S. currency's performance against a basket of six major currencies, rose 0.4 percent to 82.403, rebounding from a four-week trough of 81.876 marked on Monday.
U.S. financial markets were closed on Monday for the Labor Day holiday and will resume trading later in the day.
The dollar slipped 0.1 percent against the yen to 84.10 yen, remaining within sight of a 15-year low of 83.58 yen hit last month, as investors stay keen to buy safe-haven currencies, such as the Japanese currency and the Swiss franc.
The Bank of Japan took no new policy steps at a meeting on Tuesday.
The central bank boosted its cheap loan scheme at an emergency meeting last week, bowing to government pressure for steps to protect a fragile recovery after the yen surged to a 15-year high against the dollar, though the move's impact has been limited.
The greenback could slip further, given expectations that the BOJ will take no additional easing steps in the near term, while wariness over possible market intervention by Japanese authorities to rein in the yen's gains is keeping speculators cautious about aggressively taking long yen positions, traders said.
The euro slid 0.6 percent against the yen, to 107.65 yen, although it was still well above a nine-year low of 105.44 yen reached in late August.
The euro was down 0.8 percent versus the Swiss franc at 1.2925 francs, crawling towards an all-time low of 1.2850 francs struck on Aug. 31.
The Australian dollar dipped 0.4 percent on the day to $0.9130, having slipped from a four-week high of $0.9181 hit on Monday.
The Reserve Bank of Australia kept rates at 4.5 percent as expected on Tuesday. While the central bank is generally upbeat on the Australian economy, it mentioned some uncertainty about overseas.
"For the Aussie dollar to rise beyond $0.92, the global economy will need to gather more strength," said Ayako Sera, market strategist at Sumitomo Trust Bank.
The Australian currency eased further after two key independent lawmakers backed the Labor party, giving Prime Minister Julia Gillard the majority she needs to form a government.
(Additional reporting by Charlotte Cooper and Hideyuki Sano; Editing by Joseph Radford)