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* Investors greet steady Fed with cautious optimism
* Shares of banks, property firms up after Fed decision
* Euro rises to record high vs yen ahead of ECB meeting
By Kevin Plumberg
HONG KONG, June 26 (Reuters) - Asian stocks edged up on Thursday from a three-month low after the Federal Reserve kept rates steady while the euro hit a record high against the yen on the prospects for a euro zone rate rise.
Stocks were buoyed by Fed comments downplaying the potential for a deeper U.S. economic slowdown, but uncertainty about inflation kept gains in check and fuelled a rally in the euro against the yen on expectations that the European Central Bank would raise rates next week.
The U.S. central bank signalled on Wednesday it was in no hurry to raise rates any time soon, supporting government bond prices that had been sold off sharply on expectations central banks around the world would tackle price pressures aggressively.
Still, given that oil prices remain above $130 a barrel and persistent rises in food prices, investors were cautious about the outlook for the region.
"We've probably seen the worst, but how much better it's going to get in the short term is questionable," said Tony Russell, senior equities adviser at ABN AMRO Morgans in Sydney.
Japan's Nikkei share average <
> rose 0.4 percent, on track to break a string of five sessions of losses.Hong Kong's Hang Seng index rose 0.9 percent <
>, with China Mobile <0941.HK> providing the biggest lift.Local property firms also boosted the index, in a relief rally after the Fed's stance eased concerns about sudden increase in borrowing costs.
The MSCI index of stocks in the Asia-Pacific region <.MIAPJ0000PUS> outside of Japan rose 1.1 percent, while the pan-Asia index gained 0.6 percent <.MIAS00000PUS>. Both indexes hit the lowest since March on Wednesday.
Stocks in Australia led Asia higher, gaining 1.5 percent <
>. The country's four largest retail banks, which have been beaten up in recent sessions led the index higher, with Commonwealth Bank of Australia <CBA.AX> providing the biggest lift.OIL STEADIES AFTER FALL
Japanese government bond yields, which move inversely to prices, dipped as investors scaled back expectations for Bank of Japan interest rate rises in the wake of the Fed's less-hawkist-than-expected policy decision.
The benchmark 10-year yield <JP10YTN=JBTC> dipped half a basis point to 1.670 percent, holding near a one-month low of 1.665 percent struck the previous day.
The two-year yield <JP2YTN=JBTC> dropped 1.5 basis points at 0.835 percent.
The euro hit a record high against the yen as investors looked at the potential for a widening gap between ECB and Japanese interest rates.
The ECB has maintained a hawkish stance against inflation, raising expectations it could increase interest rates next week. Bank of Japan rates are seen on hold for a while.
The euro climbed above 169.20 yen <EURJPY=>, its highest level against the yen since the single European currency was launched in 1999.
The U.S. dollar also gained against the yen, up 0.2 percent at 108 yen <JPY=>. The euro was largely unchanged against the dollar at $1.5663 <EUR=>.
Oil steadied above $134 a barrel on Thursday after dropping more than $2 on Wednesday as U.S. government data showed a surprise increase in domestic crude stocks last week.
"The surprise rise in U.S. crude stocks has pointed to a weakening demand outlook in the U.S.," said Gerard Burg, a commodities analyst at National Australia Bank in Melbourne.
"The market will focus on the U.S. economic data due later today to get a clearer picture of the economy and its impact on oil demand."