Views that the Swiss National Bank had bought euros to weaken the Swiss franc had also supported the common currency on Thursday.
The euro has seen some sharp swings in recent sessions, having tumbled earlier in the week after the European Central Bank stunned investors by taking a hard-line stance, saying it would not accept Greek bonds as collateral.
Read MoreGartman: Germany won't let Greece leave the euro zone
Greece's aid deadline with the European Union, the ECB and International Monetary Fund "troika" expires on Feb. 28.
"The Greek situation will remain a key factor at least until the Feb. 28 aid deadline. The development is likely to peak next week, giving time for at least one more round of upsets for the market," said Junichi Ishikawa, market analyst at IG Securities in Tokyo.
"For now we can turn away from Greece and focus on U.S. jobs data, which may provide an opportunity to slow the unwinding of dollar-long positions that has been taking place," Ishikawa said.
Another solid U.S. payroll reading, coupled with a possible rebound in wage growth, may revive recently-flagging views that the Federal Reserve might consider raising interest rates as early as mid-year and favour the dollar.
Non-farm payrolls probably increased 234,000 last month after advancing 252,000 in December, according to a Reuters survey of economists. It would be the 12th straight month of job gains above 200,000, the longest streak since 1994.
Callum Henderson, global head of FX research for Standard Chartered Bank in Singapore, said Standard Chartered's baseline expectation is that non-farm payrolls will increase by around 260,000.
The market could show a sharp reaction if the increase in non-farm payrolls turns out to be either less than 200,000, or more than 300,000, Henderson said, adding that such results could lead to "quite a bit of volatility".
The dollar index, which measures the greenback's value against a basket of major currencies, held steady at 93.556. The dollar index has retreated over the past couple of weeks after hitting an 11-year high of 95.481 on Jan. 23.
Against the yen, the dollar sagged 0.2 percent to 117.32 yen, staying within a range of roughly between 116.00 yen to 119.00 yen seen since mid-January.
The Australian dollar rose 0.4 percent to $0.7827, gaining a lift after the Reserve Bank of Australia's quarterly statement did not sound as dovish as some had expected.