"The market's focus was distracted away from Greece last week with the UK elections and the (U.S.) payroll data," said Richard Scalone, co-head of foreign exchange at TJM Brokerage in Chicago. "The second that was out of the way, (investors) jumped on it."
U.S. non-farm payrolls data released last Friday was mixed.
Scalone said investors saw some risk of a Greek default. The chances that Greece will leave the eurozone are slightly less than one in four, according to a Reuters poll of traders, but if Athens defaults on the IMF loan on Tuesday, the likelihood will increase.
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The dollar benefited from the jitters over Greece and was on track to notch its third straight session of gains against the euro. The dollar index, which measures the greenback against a basket of six major currencies, was also set to post its third straight session of gains.
The New Zealand dollar looked set to post its biggest one-day decline against the greenback since late January as speculation that the country's central bank could cut rates gathered momentum. The New Zealand dollar set a 7-1/2-week low of $0.7355 against the U.S. dollar in U.S. trading.
"Dovish rhetoric by the (Reserve Bank of New Zealand) and the fixed income market pricing in a further 50 basis point cut by the end of the year is putting pressure on the kiwi," said Dean Popplewell, chief currency strategist at Oanda in Toronto.
The euro was last down 0.58 percent against the dollar at $1.1156 after hitting a more than two-month peak of $1.1392 last week. The dollar was up 0.30 percent against the Swiss franc at 0.9342 franc and was up against the yen at 120.13 yen.
The dollar index was up 0.23 percent at 95.01.