* European shares edge high as ECB momentum continues
* Euro money market rates hit lowest on record, euro drops
* Dollar index edges up on higher yields
* Carry trades keep Aussie near 6-mth high vs euro
By Marc Jones
LONDON, June 10 An all-time low for euro zone money market rates bolstered the region's bond rally and held down the euro on Tuesday, providing clear proof that the European Central Bank's latest support measures are gaining traction.
The steady drip-feed of global stimulus also kept world shares inching towards an all-time high as a record high Wall Street and a three-year peak for Asia left them looking for a fifth day of back-to-back gains.
U.S. stocks were was expected to take a breather when trading resumes later, but European stocks continued to shuffle forward.
Germany's Dax had secured a firm hold above the psychological 10,000 points level as afternoon trade began, while a government reshuffle in Greece helped shares extend their gains over the past weeks to a staggering 25 percent .
Last week's ECB cut in interest rates and its move to start charging banks who park spare cash ensured the impact continued elsewhere too.
The euro tumbled back towards a four-month low against the dollar at $1.3540, while there were new lows for Portuguese and Irish borrowing costs , two of the countries bailed out during the euro debt crisis.
The rate banks in the euro zone charge one another to borrow overnight - known as EONIA - hit an all-time low of 0.053 percent too, a move the ECB will hope will feeds to firms and consumers, boosts growth and prevents deflation setting in.
"Broadly what the ECB has done has been pro-risk," said Alvin Tan, a currency strategist at Societe Generale in London.
"Quite apart from the currency moves we have seen, volatility is just plunging and that is all part of the story."
The global appetite for riskier assets has also been whetted by last week's upbeat U.S. non-farm payrolls jobs report.
Wall Street resumes later with the S&P 500 on a run of four straight record closes and the Dow on its third.
Aside from the ECB's recent bold moves, there was other reassuring news from the euro zone on Tuesday too.
Italian industrial output rebounded more than expected in April, and although France's recovery, which is lagging that of its euro zone peers, only marginally improved, Barclays said the ECB's latest moves may have had a positive impact on inflation expectations.
"Admittedly, this is based on two days' reaction, but it appears that the ECB is succeeding towards their goal," Barclays' Chris Walker and Marvin Barth said.
In Asia, there was more muted market reaction to Chinese inflation data as it remained well within the government's comfort zone, giving room for the government to launch fresh stimulus measures if needed to support the economy.
China's consumer prices rose 2.5 percent in May from a year earlier while producer prices fell 1.4 percent.
"No surprises again from May inflation data. Producer prices stabilised ... pointing to muted inflationary pressure," said Andy Ji, senior Asian currency strategist at Commonwealth Bank of Australia in Singapore.
Nevertheless, the risk appetite remained strong with MSCI's broadest index of Asia-Pacific shares ex Japan ending up 0.6 at its highest since June 2011.
Chinese, Indonesian and Korean shares all rose more than 1 percent, though Tokyo's Nikkei and stocks in India bucked the trend as investors cashed in on some of the sizeable gains both have seen recently.
Among the major currencies, the dollar continued to benefit from rising U.S. Treasury yields as the benchmark 10-year rate topped 2.62 percent.
The dollar index, which measures the greenback's strength against a basket of key currencies, climbed 0.2 percent after a similar gain on Monday, though it was slightly lower on the day against the yen at 102.32.
Yield hungry investors also piled into carry trades, pushing the Australian dollar to a near a six-month high against the euro with also gave a lift to its antipodean cousin the kiwi dollar.
In commodities, the wave of risk appetite sweeping through markets kept safe-haven gold pegged down at $1,254.60 an ounce and pushed up Brent oil 30 cents to $110.30 a barrel.
A breakdown in strike talks in South African pushed platinum to a 3-year high while fears about a crackdown into metal financing in China sent copper to a new one-month low. (Editing by Alison Williams)