The euro was off its session lows but still sharply down on the day in Asian trading on Monday after Greece failed to strike a deal with its lenders, taking it a step closer to a debt default that could force its exit from the euro zone.
The Swiss and Japanese currencies, both of which often appreciate during times of uncertainty on their perceived safe-haven status, were broadly higher, while the dollar notched a three-week high against a basket of currencies.
(READ MORE: South Africa’s rand on back foot as Greece woes hit EM)
The euro EUR=EBS fell to a one-month low of 1.0955 US dollars on the EBS trading platform, from around 1.1165 US dollars late on Friday. It had last recovered to 1.1010 US dollars, still down about 1.4 percent on the day.
"It looks like a bit of stability has returned after the earlier onslaught, so I'd say there was a bit of profit-taking, given that we are very much in a state of flux," said Sue Trinh, senior currency strategist at RBC Capital Markets in Hong Kong.
"Headline risk remains quite acute, with the focus squarely on Greece," she said.
Against the Swiss franc EURCHF=R, the euro fell as low as 1.0256 francs according to Reuters data, its weakest level since late April, and was last buying 1.0331 francs. The euro also plumbed a one-month low around 133.80 yen EURJPY=EBS on EBS, and was last at 135.33 yen, down about 2.1 per cent.
The dollar JPY=EBS fell to a one-month low of 122.10 yen before pulling away from a test of the 122 level. It last stood at 122.86 yen, off 0.8 per cent.
The dollar index, which tracks the greenback against a basket of six major rival currencies, added about 0.7 per cent on the day to 96.170 .DXY, after earlier rising as high as 96.369, its highest since June 8.
"Ahead of the weekend, there seemed to be a market consensus that something would get done for Greece, so it was a rare occasion when the market takes position for the optimistic view," said Bart Wakabayashi, head of foreign exchange for State Street Global Markets in Tokyo.
Japanese Finance Minister Taro Aso said on Monday he did not think the yen would suddenly spike or Japanese stock declines would spread due to turmoil triggered by Greece's deepening crisis.
The Bank of Japan is not considering offering emergency liquidity, though it stands ready to act if the Greek crisis were to trigger global market turmoil, sources told Reuters.
But the likelihood of a Greek default on a 1.6 billion-euro payment to the International Monetary Fund by a Tuesday deadline appeared greater after Athens effectively rejected proposals made by its European lenders in exchange for more credit at last-minute bailout talks at the weekend.
Greek Prime Minister Alexis Tsipras shocked European officials by instead calling for a referendum to be held on July 5 to ask Greek voters to decide whether to accept the bailout terms which his government opposes. Athens also closed banks and imposed capital controls to prevent a collapse of its banks as anxious investors pulled out their cash.
Given relatively low liquidity as investors cut their euro positions, Wakabayashi said the single currency's drop so far did not suggest any panic selling in the foreign exchange market.
"It's been surprisingly orderly, as the reaction was expected because of the headlines over the weekend. It could have been much uglier," he said.
(READ MORE: Greece defies creditors, seeking credit but no bailout)
Some investors had begun paring bets on the euro even before the situation reached its latest crisis point, according to Reuters calculations and data from the Commodity Futures Trading Commission released on Friday. Net short positions in the euro increased to 99,306 contracts in the week ended June 23 from the previous week's 89,357 contracts, which was the smallest level of net euro short positions since late July.
A Greek default could set it on a path out of the euro zone, which many investors fear could fatally weaken the entire currency bloc.
Analysts said that in addition to increasing uncertainties about Greece's future in the euro zone, the vote would raise political risks for Tsipras's government if the public votes in favor of accepting the bailout proposals.
With Greece's woes in the spotlight, the timing of the U.S. Federal Reserve's move to raise interest rates is even more cloudy. Most economists had seen the Fed hiking rates in September, but those expectations could be pushed back if a Greek exit from the euro zone were to roil financial markets and possibly even dent global growth.
Federal Reserve chair Janet Yellen has said that any decision to lift interest rates would rest on labor market improvement. Economists polled by Reuters expect the next nonfarm payrolls report, to be released on Thursday because of Friday's July 4 holiday, will show the U.S. economy added 232,000 jobs in June after May's unexpected 280,000 surge.