Late on Monday a Greek government official denied a German newspaper report that there is a plan for Greece to impose capital controls if further debt talks fail to reach a solution. The euro did not move on the Greek knockdown of the report, which was seen as contributing to a brief euro sell-off before it resuming its upward advance on the greenback.
Read MoreGreece on 'brink of disaster;' calls emergency meeting
European Central Bank President Mario Draghi said on Monday the economy was recovering at a moderate pace and that a strong and credible agreement with Greece is in the interests of the euro area as a whole but the ball is in Greece's court.
Concerns that Greece could default and leave the euro zone prompted the first significant bid for safety in German Bunds in six weeks and lifted peripheral euro zone bond yield premiums to their highest in nearly seven months.
Reuters data showed that one-month euro/dollar implied volatility, a gauge of how sharp swings in the currency are likely to be, rose to a 3-1/2 year high of 14.305 percent. "As the quarter winds down we are kind of in a no-man's land, where choppy consolidative trade prevails," said Marc Chandler, global head of currency strategy at Brown Brothers Harriman in New York.