The U.S. dollar climbed against its major rivals in the European session on Monday, after the New York Fed President William Dudley said that inflation is little lower than the Fed's target but it would rise along with a pick up in wage growth, enabling the central bank to continue the tightening cycle.

"We are pretty close to full employment. Inflation is a little lower than what we would like, but we think that if the labor market continues to tighten, wages will gradually pick up and with that, inflation will gradually get back to 2 percent," Dudley said at a speech to chamber of commerce in Plattsburg, New York.

Reversing from an early low of 110.70 against the Japanese yen, the greenback climbed to 111.34.

The greenback that slipped to 5-day lows of 1.2814 against the pound and 0.9696 against the franc bounced off to 1.2772 and 0.9729,respectively.

The greenback advanced to 1.1177 against the euro, following a 4-day decline to 1.1213 at 7:00 am ET.

The next possible resistance for the greenback is seen around 112.5 against the yen, 0.98 against the franc, 1.10 against the euro and 1.25 against the pound.

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