Investors bought the safe-haven dollar, pushing the dollar index against major currencies to a 7 1/2 month high.
"It is the risk-of-capital flight out of Cyprus that is worrying," said Mankash Jain, head of FX and investment management at hedge fund Solo Capital in London. "Investors would want to hold the dollar or German Bunds in such a scenario. We see the euro going only one way—and that is down."
EU and ECB officials have sought to quash the suggestion that the Cyprus bank restructuring was a template for future bank bailouts in the euro zone.
The spread between the yields on two-year U.S. Treasuries and their German counterparts has widened to its highest since late December in favor of the former. That is likely to support the dollar, traders said.
"Cyprus is certainly still weighing on the euro, but the bulk of the move lower today was triggered by the Italian debt auction," said Greg Anderson, G10 strategist at CitiFX, a division of Citigroup in New York.
"Rising Italian borrowing costs and its political situation are both negatives," he said. "Investors are not overly short the euro, so there is plenty of scope for the euro to test the lows of the past cycle."
Upcoming BOJ Meeting Eyed
The yen fared well against the euro as investors preferred the safest, most liquid currencies, given the troubles in the euro zone. The euro last traded down 0.66 percent at 120.63 yen.
Against the dollar, the yen should continue to weaken on the prospect of aggressive monetary easing measures by the Bank of Japan next week. The Nikkei Business Daily said the central bank will boost bond buying at its meeting on April 3-4.
(Read More: Ssshh! Why Japan Is Keeping Quiet on the Yen)
Sources also told Reuters the BOJ would likely start open-ended asset purchases immediately rather than in 2014, as originally agreed in January, and also buy longer-dated bonds.
But with aggressive easing by the BOJ widely expected, there is a risk that it could fall short and then the yen could recover some lost ground.
The dollar last traded at 94.43 yen, up just 0.02 percent for the day, according to Reuters data.