The U.S. dollar traded lower against the most major currencies after the weaker-than-expected U.S. factory orders. Factory orders in the U.S. dropped 3.4% in December, missing expectations for a 1.8% decrease, after a 1.7% decline in November. That was the fifth straight decline.

November's figure was revised down from a 0.7% fall.

Manufacturing in the U.S. is cooling due to weak global demand and falling oil prices.

The euro rose against the U.S. dollar as the new Greece government outlined its plans to renegotiate the terms of its bailout, retreating from demands for a debt haircut. Greek Finance Minister Yanis Varoufakis has proposed debt swaps.

Eurozone's producer price index dropped 1.0% in December, missing expectations for a 0.7% decrease, after a 0.4% decline in November.

The British pound traded higher against the U.S. dollar. Markit's and the Chartered Institute of Purchasing & Supply's construction purchasing managers' index (PMI) for the U.K. rose to 59.1 in January from 57.6 in December, beating expectations for a decline to 56.9.

The Canadian dollar traded higher against the U.S. dollar despite the weaker-than-expected Canadian raw materials purchase price index. The Raw Materials Price Index (RMPI) dropped 7.6% in December, missing expectations for a 4.6% fall, after a 5.7% decline in November. November's figure was revised up from a 5.8% decrease.

The drop was driven by lower prices for crude energy products.

The Swiss franc traded higher against the U.S. dollar. Switzerland's trade surplus narrowed to CHF1.5 billion in December from CHF3.8 billion in November.

Exports rose 7.2% in December, while imports declined 0.2%.

The New Zealand dollar increased against the U.S. dollar. In the overnight trading session, the kiwi fell against the greenback in the absence of any major economic reports from New Zealand. The interest rate cut by the Reserve Bank of Australia (RBA) weighed on the kiwi.

The Australian dollar traded higher against the U.S. dollar. In the overnight trading session, the Aussie dropped against the greenback as the RBA cut its interest rate to a new record low of 2.25%, down from 2.50%. The RBA said that the Aussie remains overvalued.

The RBA Governor Glenn Stevens said in a statement that the Australian dollar remains "above most estimates of its fundamental value", despite the recent decline. He pointed out that a lower exchange rate is needed "to achieve balanced growth in the economy".

Australia's trade deficit narrowed to A$0.44 billion in December from A$1.02 billion in November. November's figure was revised down from a deficit of A$0.93 billion. Analysts had expected the trade deficit to decrease to A$0.85 billion.

Exports increased 1.0% in December, while imports declined 1.0%.

Building approvals in Australia declined 3.3% in December, beating expectations for a 4.8% decline, after a 7.7% increase in November. November's figure was revised up from a 7.5% gain.

The Japanese yen traded lower against the U.S. dollar. In the overnight trading session, the yen traded higher against the greenback. Japan's monetary base increased 37.4% in January, missing expectations for a 40.1% rise, after a 38.2% gain in December.