The euro fetched $1.2390 and 97.19 in Tokyo afternoon trade, against $1.2381 and 97.30 yen in New York late Friday.
The dollar bought 78.44 yen against 78.59 yen.
In early trade Monday, the euro briefly reached $1.2442, its highest level in a month, after the US Labor Department said the economy created 163,000 jobs in July, well above forecasts of 100,000 jobs, sending Wall Street surging.
Mansoor Mohi-uddin, UBS head of forex strategy, said the euro could climb past the $1.25 level, but the rise would be unsustainable given the likelihood of fresh policy action by the European Central Bank (ECB).
"We maintain our longer term $1.1500 target as ECB balance sheet expansion will cyclically weaken the currency again -- even if structural concerns about the eurozone breaking up are reduced," Mohi-uddin said.
Credit Suisse analyst Hiromichi Shirakawa said the upbeat US data made it less clear that the US Federal Reserve would usher in further monetary easing at a policy meeting on September 13.
"We see a rising possibility that the Federal Reserve holds off its decision on additional action until December or early next year," he said in a note.
The dollar dropped against other Asia-Pacific currencies.
It fell to Sg$1.2414 from Sg$1.2481 on Friday, to 55.26 Indian rupees from 56.15 rupees, and to 1,126.70 South Korean won from 1,135.40 won.
It also sank to 41.79 Philippine pesos from 41.93 pesos, to 9,465.00 Indonesian rupiah from 9,476.00, to 31.48 Thai baht from 31.62 baht, and to Tw$29.93 from Tw$30.00.
The Australian dollar rose to $1.0563 from $1.0475 while the Chinese yuan bought 12.29 yen against 12.24 yen.