The euro and other currencies will be in a holding pattern until the outcome of Greece's weekend referendum becomes clear, according to analysts.
The euro has recovered from Monday's steep plunge against the US dollar while the Australian dollar - which also fell, but not to the same extent - continues to fluctuate around the 76.7 US cent mark.
The European currency was trading at $US1.12 on the weekend but dropped to $US1.0975 on Monday as fears that Greece would have to exit the euro took hold.
It then bounced back to $US1.1243 on Monday night - a seven-day high - before settling back at the $US1.12 level in late local trade on Tuesday.
"There was a lot of illiquidity into the market and a lot of uncertainty," said ANZ currency analyst Daniel Bean.
"But as the day went on people became marginally more confident that ... any default of Greece would not turn into anything that was systemic."
Mr Bean said the European Central Bank had a range of measures available to deal with the crisis, including front-loading the ongoing quantitative easing program.
"The market took a little bit of heart that we've been planning for this crisis for four years now and there are a number of measures in place," he said.
Mr Bean said the bounce to a seven-day high illustrated how the crisis was driving volatility in Europe and around the world. "Be wary of buying risky currencies and the euro," he said.
Overall, Europe's fundamentals, including soft inflation data released on Monday, still pointed to a lower euro, he said.
"In Europe, quantitative easing is going to be an ongoing prospect with or without Greece."
The Australian dollar was overwhelmingly following overseas trends, he said.
"The domestic story is relatively benign. We are looking to the global economy and global dynamics for direction."
The topside of the Australian dollar was capped by the US Federal Reserve and the tepid US recovery, said Mr Bean, but the Aussie could head below its late Tuesday level of US76.68¢.
"We would need higher volatility and something big offshore in order to drive a fresh low."
ThinkForex markets analyst Matt Simpson said he was surprised the euro had reversed as successfully as it had done.
"I thought that it would continue downwards", he said. "Bond holders in Italy, Portugal and Spain panicked because they were worried about contagion so they got rid of their bonds put the bond yields up and that in turn added a bit of support for the euro."
US non-farm payrolls - which has been brought forward to Thursday because of the US independance day holiday - would normally dominate the week for currencies, but this week is all about the referendum, said Mr Simpson.
"It's about the referendum and so I think we're going to see holding patterns across a lot of the major currencies this week."
The Australian dollar "had defended US76¢ pretty well," said Mr Simpson.
"If there is a resolution and the Greeks vote yes and the package gets through, you would probably see a stronger euro and the Aussie would follow suit."
However, "my gut feeling is that they will say no out of pride amd dignity." A no vote will send both the euro and the Australian dollar lower against the greenback, he said.
