The euro held firm last week after three straight days of gains at $1.18455 (EUR=).
The common currency was supported after the European Central Bank showed no apparent sign of stemming the single currency's appreciation.
Still, it faces an uphill battle in tackling the $1.20 barrier, with investors wary euro zone policy makers may not want to see the currency strengthen much beyond that level.
Some euro zone countries, such as France and Spain, are reporting rises in coronavirus infections, in contrast to falls in the United States, clouding the outlook for economic recovery.
The dollar's index against a basket of currencies stood little changed at 93.317 (=USD), with focus on the Federal Reserve's policy announcement on Wednesday.
Expectations of further monetary easing by the Fed have been a drag on the dollar. The dollar index has lost more than 4% so far this quarter.
The Fed has announced late last month that it has adjusted its policy strategy, noting that it wants inflation to average 2% over time. But some analysts say markets may have gone too far in expecting further Fed stimulus.
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