Risk reversal spread of the euro/dollar widened in favor of euro/dollar puts to the highest level in about two months, suggesting many investors want to hedge against the euro's fall.
As investors sought shelter from possible turmoil in the euro, it was the British pound that benefited from some safe-haven buying.
The pound on Tuesday rose to a two-week high against the euro of 71.75 pence per euro. It last stood at 72.00.
Sterling kept its firm tone against the dollar as well, hitting a four-week high of $1.5655, having risen almost five cents from its low so far this month of $1.5170. It last was at $1.5642.
The dollar held firm against most other currencies as investors expect Fed policymakers to intimate that U.S. interest rates will start rising later this year after news of U.S. housing permits for future construction surging to a near eight-year high.
"The latest economic data is showing improvement so how the Fed perceives them will be a key. We suspect the Fed will acknowledge the improvement, concluding the weakness in January-March was temporary," said Shin Kadota, chief strategist at Barclays in Tokyo.
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The Fed statement is due at 1800 GMT, followed half an hour later by Chair Janet Yellen's news conference where analysts assume she will focus on signs the economy is recovering after a bumpy start to the year.
There will be particular attention on the Fed's median forecast for the funds rate over 2015 which could be trimmed from the previous 0.625 percent, in line with Yellen's assurance that any tightening cycle will be very gradual.
The dollar's index against a basket of major currencies stood at 94.881, off Tuesday's low of 94.557.
Against the yen, the dollar traded flat at 123.45 yen, with support seen at around last week's low of 122.46 yen.
Traders are reluctant to bid the dollar aggressively, however, after Bank of Japan Governor Haruhiko Kuroda surprised the markets last week by saying the yen is unlikely to weaken further.
There are few Asian economic indicators due on Wednesday, with markets' now firmly focused on the Fed's policy meeting and developments in the Greek debt crisis.