Traders said the next few days could be crucial. Euro-area leaders and finance ministers met in Brussels to discuss Greece and there has been no resolution so far.
With Greek banks down to their last few days of cash and the ECB tightening the noose on their funding, Greek Prime Minister Alexis Tsipras tried to convince the euro group to authorize a new loan swiftly.
"I'd like to think both sides can find a compromise, but I'm not sure they can," said Randy Warren, chief investment officer at Warren Financial Service, in Exton, Pennsylvania.
"I think the austerity that's being asked, which is really necessary is probably too much for Greece. Greece simply cannot pay its bills. So I'm not sure this ends well."
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Since Athens missed a debt payment to its creditors and Greek voters rejected tough conditions for further bailouts, the euro has retreated from mid-June highs of $1.14, but there has been no panic selling. One reason is the expectation the ECB will take action to stabilize the market.
Against the dollar, the euro fell 0.7 percent to $1.0978 , after sliding to a five-week low of $1.0917, while the dollar index rose 0.6 percent to 96.846, after earlier hitting a one-month high.
The euro was last down 0.8 percent against the yen to 134.40 yen, after earlier dropping to a five-year trough.
Meanwhile, commodity currencies fell sharply, with the Australian dollar hitting a six-year low as Chinese stock markets went into a tailspin.
The Australian dollar, which is a proxy for Chinese investments, fell 0.7 percent to US$0.7440, with a drop in iron ore prices also weighing.
The New Zealand dollar plunged as well, falling to a five-year low against the greenback. It was last down 0.5 percent at US$0.6645. The Canadian dollar, meanwhile, hit a three-month low of C$1.2732 against its U.S. counterpart .