* Asian shares fall on risk aversion, extend losses
* Euro dips on doubts about EU's ability to tackle debt
* Nikkei edged down as foreigners extend selling
By Kevin Yao
SINGAPORE, May 12 (Reuters) - Asian stocks fell on Wednesday as investors shunned riskier bets on nagging worries about euro zone debt woes despite a $1 trillion rescue package, and such jitters weighed down the euro.
MSCI's index of Asia-Pacific shares outside Japan fell just over 0.4 percent, a day after falling just over 1 percent, following modest losses on Wall Street.
European stock index futures fell, signalling weakness for a second straight session.
Futures for the STOXX Europe 50, Germany's DAX and France's CAC-40 shed 0.4 to 1.3 percent. Britain's FTSE 100 was seen opening as much as 0.6 percent lower, financial spreadbetters indicated.
South Korean shares shed just over 0.4 percent, reacting little to the Bank of Korea's widely expected decision to keep interest rates steady, while Samsung Life Insurance trimmed gains in its debut.
"Sentiment is broadly cautious right now as concerns about southern European debt problems still linger. It could take some time before investors feel compelled to buy again," said Kim Young-june, a market analyst at SK Securities.
The Bank of Korea left its interest rate at record-low 2.0 percent for a 15th consecutive month on Wednesday.
In Tokyo, the Nikkei average was down 0.2 percent, reversing earlier gains as foreigners continued to sell Japanese stocks on concerns that the euro zone relief package did little to resolve the region's longer-term debt problems.
"Since the start of this month, foreigners have really been selling Japanese stocks, partly because Japanese markets were closed for holidays and foreign markets fell during that time, and partly because the Greek debt crisis really worsened," said Hideyuki Ishiguro, a strategist at Okasan Securities.
"At this point, I don't think a lot of this money is flowing into other Asian share markets. It's probably going into U.S. Treasury bonds and gold as part of a shift from riskier assets."
Benchmark indexes in Hong Kong fell 0.5 percent while Shanghai shares were virtually flat, but Australia advanced 0.6 percent as its federal budget boosted banks.
On Monday, the MSCI ex-Japan index climbed 3.6 percent -- its biggest single-day percentage gain since May 2009 -- fuelled by hopes that the massive rescue package would prevent Greece's debt crisis from spreading to other countries in the euro zone and possibly sparking another global credit crunch.
But the global rally quickly fizzled on Tuesday as worries resurfaced that Greece and other heavily-indebted euro zone members will not be able to deliver on promises of deep spending cuts.
EURO STRUGGLES
The euro held steady near $1.2636, down 0.2 percent from late U.S. trade, but off a 14-month low of $1.2510 hit last week.
One near-term downside target for the euro may be around $1.2580, near Friday's low, a trader said.
Sterling held its overnight gains after Conservative party leader David Cameron took over as British prime minister after securing a power-sharing agreement between his centre-right party and the smaller Liberal Democrats.
Sterling hovered near $1.4910 after rising above $1.5000 on Tuesday.
The Conservatives and the smaller Liberal Democrat party agreed on Wednesday to form Britain's first coalition government since 1945, ending uncertainty over who would take power after inconclusive elections last week.
U.S. crude futures fell 0.7 percent to above $75.82 a barrel, while spot gold hit another record high above $1,230 an ounce. (Additional reporting by Elaine Lies in TOKYO and Jungyoun Park in SEOUIL; Editing by Kim Coghill)