* Euro shakes off low inflation data
* Dollar index down after 3 days of gains (Recasts, adds quotes, updates prices, changes byline, dateline, previous LONDON)
NEW YORK, March 31 (Reuters) - The euro rose to a three-week high against the yen and firmed against the dollar despite softer-than-forecast inflation numbers that sapped hopes the European Central Bank will cut rates when it meets this week.
After three days of gains, the U.S. dollar index of major currencies was off 0.18 percent to 80.148 in late morning New York trade.
The euro, which was ahead 0.85 percent against the yen at 142.08 yen, was also up against the dollar at$1.3778 for a gain on the day against the greenback of 0.20 percent.
The shared currency was also up 0.21 percent against the British pound at 0.8282 euro on trading driven by speculation that euro zone inflation will not be soft enough to spur more monetary easing by the ECB.
Europe's central bankers worry that a euro now approaching a $1.40 level not seen since 2011 would aggravate deflationary forces and hurt economic recovery.
"It will take action by the ECB for the euro to decline," said Joe Manimbo, senior market analyst at Western Union Business Solutions in Washington. "Investors want actions."
Dealers in Europe said new bets for a weaker yen against the dollar and euro have been placed since players squared up for the end of the Japanese trading year on Thursday.
The prospect of more steps to ease monetary policy in Japan later this year at a time when U.S. officials are reining in their own money-printing argues for a stronger dollar.
"I heard on Friday that there was a chunk of U.S. money going into structures on the topside (for the dollar) and the dollar has been grinding higher since then," said Graham Davidson, a spot dealer at NAB in London.
"That has been helped by U.S. yields going a bit higher and Bunds have done the same."
Structures in market jargon refers to options betting on a move one way or another in a currency. CFTC data on positioning showed speculative bets against the yen had fallen off ahead of the last trades in the financial year in Japan ending on Monday.
The market also now looks doubtful about any action by the ECB to ease policy further this week.
Data on Monday showed inflation sank to just 0.5 percent in March but, as Bundesbank chief Jens Weidmann underlined on Saturday, much of the fall has been due to one-off drops in energy and food prices over which the ECB has little control.
The common currency continues to be supported by a return of cash to bond markets in the euro area's southern half as well as Germany's huge current account surplus, helping it to buck forecasts of a stronger dollar this year.
"The euro got trashed around the inflation numbers but then came roaring back," Davidson said.
"I think the market has probably priced in the story on the fall in inflation. The bottom line is that the economy is recovering and my hunch would be that the bank does nothing." (Additional reporting by Patrick Graham in London; Editing by James Dalgleish)