European Central Bank President Mario Draghi recently made clear the euro's strength is a possible trigger for the central bank to ease monetary policy. He is scheduled to give a speech in Amsterdam on Thursday.
ECB executive board member Benoit Coeure said on Tuesday there was further margin to reduce the main interest rate below 0.25 percent and that the strength of the euro could be keeping inflation too low.
But until the ECB takes action, possibly at its next meeting on May 8 in Brussels, traders said the euro would stay rangebound.
The euro slipped to a two-week low before rebounding to trade slightly higher around $1.38.
Investors await Wednesday's euro zone 'flash' PMI surveys while the German IFO institute's monthly reading of business sentiment in Europe's largest economy is due Thursday.
Very weak inflation in the euro zone, due partly to the strong exchange rate, raises pressure on the ECB to further loosen monetary policy to stimulate growth.
In recent weeks Draghi has brought the currency into focus and warned any further strengthening could lead the euro zone's central bank to use unconventional tools such as asset purchases.
On the other hand, analysts said the dollar was starting to look attractive on the back of improving U.S. data and earnings.
The dollar was unchanged at 102.61 yen, after hitting its best level since April 8 of 102.73 yen.