Hopes that a European Central Bank rate cut will lead the eurozone to recovery gave the single currency room to post gains.
In U.S. trading on Friday, EUR/USD was up 0.30% at 1.3104, up from a session low of 1.3034 and off from a high of 1.3159
The pair was likely to find support at 1.3034, the earlier low, and resistance at 1.3242, Thursday's high.
The Bureau of Labor Statistics reported earlier that the U.S. economy picked up 165,000 nonfarm payrolls in April, up from 138,000 in March, whose figure was revised up from 88,000.
May's figures far outpaced analysts' forecasts for a 145,000 figure.
Also fueling appetite for risk-on asset classes, February's figures were revised to 332,000 from 268,000.
The headline unemployment rate ticked down to 7.5% in April from 7.6% in March.
The euro also saw demand on hopes recent ECB action will spur recovery.
The European Central Bank cut interest rates by 25 basis points this week.
The euro, meanwhile, was up against the pound and up against the yen, with EUR/GBP trading up 0.16% at 0.8424, and EUR/JPY trading up 1.53% at 129.83.