In U.S. trading on Tuesday, EUR/USD was down 0.25% at 1.2818.
The eurozone unemployment rate hit an all-time high of 12% in February, up from January's original 11.9% reading, which was revised up to 12%.
The numbers sparked safe-haven demand for dollar as did eurozone factory data.
The eurozone’s manufacturing purchasing managers’ index hit 46.8 in March, according to Markit Economics, up from a final reading of 46.6 in February but still well below the 50 mark that separates growth from contraction.
The manufacturing PMI in Germany, Europe's economic engine, came to 49.0 in March from a final reading of 48.9 in February, which gave the euro some support.
Many market participants remained on the sidelines ahead of the European Central Bank’s upcoming policy meeting on Thursday.
While no changes to monetary policy are expected, many remained in wait-and-see mode ahead of ECB President Mario Draghi's press conference that will take place when the policy meeting concludes.
Across the Atlantic in the U.S., factory orders rose 3.0% in February, above expectations for an increase of 2.9%, according to the Census Bureau.
The numbers supported the greenback.
The greenback, meanwhile, was up against the pound, with GBP/USD trading down 0.85% at 1.5103.
Data released earlier revealed that the U.K. manufacturing PMI rose to 48.3 in March from 47.9 in February, missing expectations for a reading of 48.5, which rekindled talk of that the Bank of England may restart its asset purchase program soon, possibly this week.
The dollar was up against the yen, with USD/JPY trading up 0.23% at 93.45, and up against the Swiss franc, with USD/CHF trading up 0.31% at 0.9494.
The dollar was down against its counterparts in Canada, Australia and New Zealand, with USD/CAD down 0.17% at 1.0149, AUD/USD up 0.21% at 1.0444 and NZD/USD trading up 0.52% at 0.8414.
The dollar index, which tracks the performance of the greenback versus a basket of six other major currencies, was up 0.25% at 83.11.
On Wednesday in the U.S., payroll processor ADP will release its monthly report on private-sector nonfarm payrolls, a precursor to the official jobs report due for release on Friday.
The U.S. is also to produce official data on crude oil stockpiles, while the ISM is to release a report on service-sector activity, a leading indicator of economic health.