Trading volumes dwindled later as U.S. markets were closed for the Labor Day holiday. In Latin America, the biggest mover was the Chilean peso, which weakened 0.6 percent against the dollar after the country's central bank said it considered cutting interest rates by more than it actually did last month.
Read MoreUkraine's Poroshenko says close to point of all-out war with Russia
Data on Monday showed factory activity across the euro zone cooled in August as the conflict between Russia and Ukraine took its toll.
The PMI survey for Germany, Russia's biggest trade partner in the European Union, fell to an 11-month low, while the index for France fell further below the 50 mark that separates expansion from contraction.
Ukrainian President Petro Poroshenko warned a ``full-scale war'' was imminent if Russian troops continued an advance in support of pro-Moscow rebels as Europe and the United States threatened Russia with new sanctions.
Analysts said the risk to euro zone growth posed by the Ukraine conflict and stubbornly low inflation should keep pressure on the European Central Bank to provide further stimulus at some stage, if not this week.
"There are many reasons to continue selling the euro,'' said Lutz Karpowitz, currency strategist at Commerzbank.
Read MoreEU wields Russia sanctions threat but timing vague
"First of all, the escalating situation in Ukraine, which might lead to further sanctions, thus increasing the risk of the euro zone economy being affected by the crisis. Even more important is the ECB rate meeting.''
While Commerzbank does not expect the ECB to announce asset purchases, or quantitative easing, when the governing council meets on Thursday, the uncertainty about further policy action is likely to keep the euro on the defensive, Karpowitz added.