The euro passed $1.34 for the first time in New York trading on Friday, reaching a record level of $1.3413.
Dealers showed concern about a report on the US labour market, which created just 112,000 jobs in November.
Economists had been expecting, on average, about 200,000 new jobs in November.
The figure marked a slowdown in employment growth after a surge of 303,000 new jobs in October.
The US currency has slid to a series of record lows against the euro, and to the lowest level for almost five years against the yen and for 12 years against sterling, amid worries about the US current account and budget deficits.
"While the market did not need an additional excuse to sell the dollar, non-farm payrolls proved a made-to-order number for dollar bears," said Michael Woolfolk at Bank of New York.
Steve Pearson, currency analyst at HBOS, said the payroll numbers were "a lot weaker than expected" and indicated that US jobs were not growing as much as previously thought.