At 2100 GMT, the euro was traded at $1.2835, down from $1.2940 late Thursday, sinking to levels last seen in early October.
The European unit also weakened against the yen, to 103.30 yen from 103.69 yen late Thursday.
The dollar, meanwhile, rose to 80.47 yen from 80.13 yen, and earlier had hit 80.68 yen, its highest level since late April.
"The US dollar is firmer overall following an encouraging US October jobs report," said Nick Bennenbroek, head of currency strategy at Wells Fargo Bank.
The United States added 171,000 jobs last month, well above the consensus estimate of 125,000, while the jobless rate edged up to 7.9 percent as the labor force grew.
The greenback jumped to 0.9403 Swiss francs, up from 0.9318 francs late Thursday, and rose against the British pound, which fetched $1.6020 compared with $1.6124.