* Low U.S. inflation adds to economic recovery story
* Dollar falls against euro, hits two-week lows vs yen
* U.S. current account narrows in first quarter (Recasts, adds comment, updates prices)
By Gertrude Chavez-Dreyfuss
NEW YORK, June 17 (Reuters) - The dollar weakened against the euro and yen on Wednesday as an unexpectedly small rise in U.S. inflation strengthened expectations that the Federal Reserve will keep interest rates low for some time.
The expectations on stable interest rates was a relief to investors worried about a recent surge in Treasury yields, which has raised fears that higher rates could clip an economic recovery.
The data also cut demand for dollars as a safe haven.
Traders, however, said the currency market's optimism was cautious at best, and sentiment could turn quickly on any bad piece of economic news.
"We're seeing dollar weakness because the idea is that inflation is not pretty evident right now and that is seen as a positive in terms of the growth outlook and risk appetite," said Brian Dolan, chief currency strategist at Forex.com in Bedminster, New Jersey.
Data on Wednesday showed U.S. consumer prices rose just 0.1 percent in May despite higher gasoline costs, and had the biggest decline over the past 12 months since 1950.
In midday New York trading, the euro rose 0.3 percent against the dollar to $1.3871 on electronic trading platform EBS.
The dollar fell to roughly two-week lows against the yen to 95.53 and was last at 95.58 yen, down 0.9 percent on the day.
The ICE Futures' dollar index was also lower, trading 0.1 percent weaker at 80.650.
A report that the U.S. current account deficit narrowed in the first quarter added to optimism in the currency market, even though the deficit topped market expectations. The current account gap of $101.1 billion was the smallest shortfall since the fourth quarter of 2001.
DOWNWARD TREND IN U.S. CURRENT ACCOUNT
"The current account is clearly trending downwards as domestic demand slows," said Ian Shepherdson, chief U.S. economist at High Frequency Economics in Valhalla, New York. "The speed of the decline has been helped by the drop in oil prices" in the second half of last year.
Overall, traders said moves in foreign exchange lacked conviction and most were unsure how to trade the dollar.
U.S. stocks and oil, meanwhile, traded lower for most of the session, and did not seem to be moving in tandem with the currency market.
Matthew Strauss, senior currency strategist at RBC Capital Markets in Toronto, said although the dollar was a little higher, "there is somewhat a risk aversion-bias in the market today and I think this is a spillover from the decline in equities on Tuesday."
"The currencies that underperform when there is high risk aversion are at the bottom -- the Aussie and Canadian dollar," Strauss said.
Some analysts believe recent optimism about a worldwide economic rebound was premature, and this was evident in the price action of commodity currencies such as the Australian and New Zealand dollars, which have failed a re-test this week of their highs for the year.
Commodity currencies tend to do well when the global economic outlook is upbeat on the belief that demand for oil and metals such as copper will rise as countries recover from recession.
More and more market participants have started to believe the rally in these currencies since May could have been a false dawn.
"Delusion has always been part of the market process. It always will be," said Jack Crooks, president of FX advisory firm Black Swan Capital in Florida. (Editing by Leslie Adler)