The U.S. dollar firmed against its major counterparts in early European deals on Tuesday amid rising treasury yields, as French election risk abated and the Cleveland Fed chief Loretta Mester warned against delaying the Fed's policy normalisation to check the risk of overheating of the economy.

Speaking at the Chicago Council on Global Affairs on Monday, Mester told that the Fed should remain vigilant against falling behind the curve as the economy continues to make progress in its goals.

"If we delay too long in taking the next normalization step and then find ourselves in a situation where the labor market becomes unsustainably tight, price pressures become excessive and we have to move rates up steeply, we could risk a recession," she said.

CME Group FedWatch tool shows 88 percent probability of a quarter point hike to 1.00-1.25 percent at its June 13-14 policy meeting, up from 79 percent late on Friday.

The benchmark yield on 10-year treasury rose 2.39 percent, while that of the 2-year equivalent was up by 1.33 percent. Yields move inversely to bond prices.

The week's key economic reports include producer price inflation on Thursday, as well as consumer prices and retail sales on Friday, which would shed more clues about the economy.

The currency has been trading in a positive territory in the Asian session, with the exception of the pound.

The greenback advanced to 1.0004 against the Swiss franc, its highest since April 18. The next possible resistance for the greenback-franc pair is seen around the 1.01 region.

The greenback rose to a 5-day high of 1.0903 against the euro and near a 2-month high of 113.49 against the yen,from its early lows of 1.0933 and 113.13, respectively. If the greenback extends rise,1.08 and 116.00 are possibly seen as its next resistance levels against the euro and the yen, respectively.

The greenback bounced off to 1.2935 against the pound and 1.3709 versus the loonie, from early lows of 1.2955 and 1.3687, respectively. The next possible resistance for the greenback is seen around 1.28 against the pound and 1.38 against the loonie.

The greenback that closed yesterday's trading at 0.6907 against the kiwi and 0.7382 against the aussie strengthened to a 2-day high of 0.6881 and a 4-month high of 0.7335, respectively. The greenback is seen finding resistance around 0.67 against the kiwi and 0.72 against the aussie.

Looking ahead, Canada building permits for March and wholesale inventories for April are set for release in the New York session.

At 9:00 am ET, Minneapolis Fed President Neel Kashkari speaks before the Minnesota High Tech Spring Conference in Minneapolis

Boston Fed President Eric Rosengren gives luncheon speech in New York City at 12:00 pm ET.

Dallas Fed President Robert Kaplan speaks at the Lower Middle Market Investment Summit in Dallas at 4:15 pm ET.

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