Still, the euro rose nearly 1 percent against the dollar after dropping earlier, as some investors unwound trading positions by buying the euro, according to traders.

A Greek official said Greece will miss a $1.77 billion debt repayment to the International Monetary Fund due on Tuesday, after the country's European partners shut the door on extending a credit lifeline.

Greece Prime Minister Alexis Tsipras announced bank holidays and other capital controls to keep banks from collapsing under the weight of mass withdrawals.

The euro fell sharply in response, to as low as $1.0956 EUR=EBS against the dollar, but was last trading up about 0.70 percent at $1.1239.

The yen, also a popular safe-haven currency, was up 0.45 percent against the euro at 137.69 EURJPY=EBS.

The Swiss franc was up 0.10 percent against the euro EURCHF= to 1.0415 francs after being knocked from a four-week high of 1.0315 francs by the Swiss National Bank, which said it intervened in the market to weaken the country's currency.

Worries about Greece made the euro less attractive as a funding currency for carry trades, in which investors in less volatile markets borrow the euro and then sell it to buy higher-yielding currencies, and that therefore was lifting the euro, according to Rabobank senior currency strategist Jane Foley.

The lift for the euro against the dollar from unwinding positions may be short-lived, according to BNP Paribas currency strategist Sam Lynton-Brown, who said investors with short euro positions were also booking profits on Monday.

"In any risk-off environment, like we had today, there is a squaring of positioning," Lynton-Brown said.

"However, BNP Paribas positioning analysis highlights that FX investors hold a considerably lighter short euro position now than in the past. Any squeeze is therefore likely to be less aggressive and less accelerated than we have seen in the past."

Trading was described as orderly, with investors displaying moderate worry over Europe's single currency, according to currency strategists. A move by some investors into safe-haven German Bunds showed investors were not pulling out of European assets completely, Foley said.

"A comfort level that this will not spill over and not have a devastating effect on peripheral countries has helped secure the market," said Fabian Eliasson, head of U.S. currency sales at Mizuho Bank in New York.

The dollar was generally down as currency traders awaited Thursday's U.S. employment report for June, which may help trigger a rise in U.S. interest rates.

The dollar index .DXY was last off 0.60 percent. The dollar was down 1.10 percent against the yen JPY=, and off 0.10 percent against sterling at $1.5729.

U.S. Treasury prices rose, with yields going to one-week lows after the breakdown in the Greek talks. Benchmark 10-year Treasuries notes US10YT=RR were last up 1-13/32 in price for a yield of 2.311 percent, down 16 basis points from Friday.

(reuters.com)