* 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, changes byline, dateline, previous LONDON)
By Gertrude Chavez-Dreyfuss
NEW YORK, June 17 (Reuters) - The U.S. dollar fell against the euro and yen on Wednesday as news of an unexpectedly small rise in U.S. inflation renewed hopes that a global recovery was under way, cutting demand for dollars as a safe haven.
The May price data also affirmed expectations that benchmark U.S. interest rates will remain low for some time, a relief to investors worried about a recent surge in Treasury yields, which has since abated somewhat.
"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 at a slower-than-expected pace in May despite higher gasoline costs, and fell over the past 12 months by the most since 1950.
In early New York trading, the euro rose 0.3 percent against the dollar to $1.3883 on electronic trading platform EBS.
The dollar fell to roughly two-week lows against the yen to 95.38 and was last at 95.89 yen, down 0.6 percent on the day.
The ICE Futures' dollar index was also lower, trading 0.1 percent weaker at 80.667.
The narrowing in the U.S. current account deficit in the first quarter also added to optimism in the currency market, even though it was way higher than market expectations. The current account gap of $101.1 billion was the smallest shortfall since the fourth quarter of 2001.
"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 H2 (second half) last year."
Overall, traders said moves in the currency lacked conviction and most were unsure how to trade the dollar given a mixed batch of U.S. economic data in the last few weeks. (Editing by James Dalgleish)