The euro last traded at $1.3524, down 0.4 percent on the day and below last week's peak of $1.3711, its highest since November 2011.
French President Francois Hollande called on Tuesday for a target exchange rate to protect the currency from "irrational movements," although the idea ran into immediate opposition from Germany.
The euro pared losses on comments by German government spokesman Steffen Seibert, who said the euro was not over-valued and that long-term competitiveness could not be achieved via exchange rates.
"We bought the euro on a break of $1.3500, but have since sold our position because we believe that at $1.3700-$1.400 it will bring out howls of protest from euro zone policymakers," said Boris Schlossberg, managing director at BK Asset Management in New York.
Schlossberg, who holds a neutral position on the euro, said euro/dollar strength will hinge on Germany.
"Only if and when they start to make noises about a strong euro will we see a serious correction," he said.
Against the yen the euro was last down 0.6 percent at 126.42 yen, off a 34-month peak of 127.69 touched in Asian trade, with the yen remaining under selling pressure on expectations of aggressive monetary easing in Japan.
"For now we remain in consolidation phase and the market wants to see euro zone economic fundamentals improve now that finances have stabilized," he said.
The euro is up nearly 2.5 percent against the dollar this year.
The dollar was last at 93.48 yen, down 0.1 percent on the day, according to Reuters data. The dollar reached a peak of 94.06 yen in Asian trade, its highest since May 2010.
News on Tuesday that current Bank of Japan Governor Masaaki Shirakawa will step down three weeks earlier than planned spurred the latest bout of yen selling.
"The yen seems to be a one-way train," said Tempus' Doyle. "We try to remind our clients how overvalued the yen has been for the past few years and was due for a major revaluation."
"Trying to pick the yen's bottom has been a dangerous endeavor, but I am staying short yen and will look to take profit again above 94," he said.
Japanese Prime Minister Shinzo Abe, who has put the BOJ under pressure to do more to spur the economy, has made it clear he wants a governor who will be bold in easing monetary policy.
The dollar is up about 7.8 percent against the yen this year, according to Reuters data.