In U.S. trading on Monday, EUR/USD was down 0.71% at 1.2983, up from a session low of 1.2882 and off from a high of 1.2995.
The pair was likely to find support at 1.2880, the low from Dec. 7, 2012, and resistance at 1.3107, Friday's high.
The one-time tax taking aim at Cypriot bank deposit holders as part of a EUR10 billion bailout deal sent the euro falling amid fears unease may grow since smaller depositors will be affected.
The move also spooked investors on sentiment that an era of eurozone bailouts that avoided touching bank deposits may now be ending.
The euro did erase earlier losses and found some support after parliament delayed voting on the measure and possibly soften the blow on smaller deposits.
Russia was quick to criticize the move in Cyprus, home to large amounts of Russian deposits.
The events in Cyprus served as the pair's chief steering current on Monday.
Elsewhere, the eurozone reported that its trade surplus narrowed to EUR9 billion in January from EUR10.3 billion in December.
Analysts were expecting the surplus to widen to EUR10.9 billion.
The euro, meanwhile, was down against the pound and down against the yen, with EUR/GBP trading down 0.80% at 0.8585, and EUR/JPY trading down 0.87% at 123.54.
On Tuesday, markets will continue to track events in Cyprus.
Elsewhere, the ZEW Institute will release its index of German economic sentiment, while the U.S. is to release official data on building permits, a leading indicator of future construction activity, and data on housing starts.