(Recasts after start of European trade)
* Aussie plunges after surprisingly soft CPI
* Speculation that RBA could cut interest rates again
* Fed, BOJ monetary policy decisions in focus in next 24 hrs
By Jemima Kelly
LONDON, April 27 (Reuters) - Australia's dollar plunged by almost 2 percent on Wednesday after data showed consumer prices fell unexpectedly in the first quarter, but most currencies traded in narrow ranges before a U.S. Federal Reserve policy decision later in the day.
The dollar edged down 0.2 percent against a basket of major currencies, with traders expecting the Fed to be wary of sending too strong a message on imminent policy tightening, particularly after another batch of disappointing data.
The Australian dollar fell by as much as 1.8 percent in early European trading, hitting a nine-day low of $0.7606 and on track for its biggest one-day fall in three months.
Data showed that core inflation unexpectedly slowed to its lowest on record in the first quarter, reviving talk the Reserve Bank of Australia could cut the already record-low 2 percent cash rate at its May policy meeting next week.
"The inflation data clearly puts an interest rate cut back on the table quite firmly," said Rabobank currency strategist Jane Foley, who is based in London.
"Whether or not that happens on May 3 or a little bit further down the line remains to be seen, but this is a central bank that targets inflation. Inflation is undershooting noticeably and therefore the logical conclusion from that is that the central bank can cut interest rates."
Markets consider it as certain that the Fed, the only major central bank to have raised rates since the financial crisis, will keep rates steady on Wednesday. The focus therefore rests on its statement and any clues it offers as to when interest rates could be hiked again.
Traders said policymakers may be wary of sending too strong a message of an imminent policy tightening, particularly after another batch of disappointing data.
"I think the Federal Reserve is getting nervous about tightening," Blackstone Advisory Partners Vice Chairman Byron Wien told reporters at a roundtable event in Tokyo.
"They...said they would tighten four times in 2016. They passed on a March increase, and I think they'll only raise interest rates once, probably in June."
Any hints that the Fed may delay an interest rate hike could leave the greenback vulnerable to more weakness against the euro and yen.
Hours after the Fed, the Bank of Japan will release its latest policy decision, on Thursday in Asia. Many market players believe the BOJ will announce some form of easing measures, including an increase in purchase of stocks and a cut in interest rates, though they think it could be a close call.
The greenback edged down about 0.1 percent to 111.16 yen. Against the euro, it slipped 0.2 percent, trading at $1.1330 versus the common currency. (Reporting by Jemima Kelly; Editing by Raissa Kasolowsky)