Donald Tusk, the former Polish prime minister who chairs the Council of EU leaders, shot back that time creates pressures for Greek talks but not the euro zone, and that it would be easy to lose everything because of bad emotions.
"The immediate knee-jerk reaction in the euro seems to be on the back of the Tsipras comments. But I don't want to oversell these moves because broadly I would expect these negotiations to be taking place right up until the 29th or 30th (of June)," said Richard Cochinos, head of Americas G10 FX strategy at Citi in New York.
"It will be going back and forth over the entire weekend and you cannot react too much to any one headline," he said.
In afternoon New York trade, the euro fell to a session low $1.1130, a loss of more than 0.5 percent. It last traded down 0.34 percent at $1.1167.
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"The comments are taking a little bit more of a contentious tone, which maybe means it is coming to a head," said Bill Samela, co-head of global FX trading at Bank of New York Mellon in New York.
"The market is finally starting to interpret the situation as being fundamental weakness in the euro zone no matter what the outcome and that will drive the euro down," said Samela.
The Eurogroup of euro zone finance ministers on Friday rescheduled their talks on Saturday three hours earlier than planned.
The euro fell 0.57 percent to 1.04345 Swiss francs.
"We may see a bit of a relief rally in the euro if there is a compromise at the weekend, but I would prefer to sell into those rallies, as there is still the case of monetary policy divergence between the euro zone and the United States," said Jeremy Stretch, head of currency strategy at CIBC World Markets.
Stretch was referring to expectation U.S. interest rates are poised to move higher while Europe and much of the rest of the world take rates in the opposite direction.
The dollar rose 0.19 percent to 123.81 yen, holding near its 20-day moving average of 123.80 yen.