The U.S. dollar strengthened against its most major counterparts in the European session on Tuesday, amid hopes that the Federal Reserve will continue to stick with its pace of rate hikes this year.

Expectations are that the Fed could raise rates three times this year, with many investors believing that the first could happen in March.

Fed funds futures are pricing in a 61.6 percent chance for a quarter-point rate increase to 1.50 percent - 1.75 percent in March, according to CME.

The markets will be looking ahead to the January policy meeting, which will help to gauge more light on the bank's plans for monetary policy tightening this year.

With today's economic calendar being relatively light, investors await U.S. import prices, producer prices, consumer inflation data and retail sales numbers due this week for more direction.

The greenback showed mixed performance in the Asian session. While it fell against the pound and the yen, it rose against the franc and the euro.

The greenback that closed Monday's trading at 1.1967 against the euro strengthened to near a 2-week high of 1.1921. The greenback is seen finding resistance around the 1.18 region.

Figures from Eurostat showed that the euro area unemployment rate declined to the lowest since 2009.

The jobless rate dropped to 8.7 percent in November from 8.8 percent in October. This was the lowest since January 2009. The rate came in line with expectations.

The greenback strengthened to a 5-day high of 1.3514 against the pound and held steady thereafter. The next possible resistance for the greenback is seen around the 1.34 area.

Data from the British Retail Consortium showed that UK non-food product sales decreased the most in five years in the fourth quarter.

In-store sales of non-food items declined 3.7 percent on a total basis and 4.4 percent on a like-for-like basis in the fourth quarter, the deepest since the records began in December 2012.

The greenback spiked up to near a 2-week high of 0.9837 against the franc, compared to 0.9772 hit late New York Monday. Further uptrend may see the greenback challenging resistance around the 0.995 mark.

Data from the Federal Statistical Office showed that Switzerland's retail sales decreased at a slower pace in November.

Retail sales fell 0.2 percent year-on-year in November, slower than the 2.6 percent decrease seen in October. This was the second consecutive decline in turnover.

The greenback bounced off to 1.2448 against the loonie and 0.7163 against the kiwi, from its early low of 1.2398 and near a 3-month low of 0.7197, respectively. The greenback is likely to locate resistance around 1.26 against the loonie and 0.70 against the kiwi.

The greenback hit a 6-day high of 0.7813 against the aussie, off its early low of 0.7865. Next possible resistance for the greenback is seen around the 0.77 area.

Data from the Australian Bureau of Statistics showed that Australia's building approvals rose a seasonally adjusted 11.7 percent on month in December, coming in at 21,055.

That beat forecasts for a decline of 1.3 percent following the downwardly revised 0.1 percent contraction in October.

On the flip side, the greenback dropped to a 5-day low of 112.50 against the yen in the early Asian session and wavered between the ranges of 112.97 and 112.64 during the European session.

Survey data from the Cabinet Office showed that Japan's consumer confidence dropped unexpectedly in December, though slightly.

The seasonally adjusted consumer confidence index decreased to 44.7 in December from November's 50-month high of 44.9. Meanwhile, economist had expected the index to rise to 45.0.

Looking ahead, at 8:15 am ET, Canada housing starts for December are set for release.

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