The euro bought $1.1194 in afternoon Singapore trade from $1.1200 in New York late Friday. It also fell to 134.40 yen from 134.56 yen.
The greenback was changing hands at 120.07 yen from 120.14 yen on Friday.
Financial markets in Japan, Thailand and Malaysia were closed for a public holiday.
“Another big week for the dollar as markets await the US non-farm payrolls report this Friday,” Phillip Futures said in a market commentary.
“A strong labour market report will likely strengthen the dollar. Conversely, weak data is likely to push the dollar down.”
Singapore’s United Overseas Bank (UOB) said the report on the US labour market could “swing market expectations for (the) Fed Reserve’s future course of interest rate actions”, referring to the US central bank.
It noted that the April jobs data is considered to be first month of non-farm payrolls untainted by the impact of the weather, meaning it would be a more realistic gauge of the health of the world’s biggest economy.
The US economy grew at just 0.2 percent in the first quarter, below market expectations, reflecting a drag from an exceptionally cold winter.
Following the slow US growth, the Federal Reserve left open its timeframe for a rise in ultra-low interest rates, making it clear it would wait for more signs of economic progress before the first rate rise in nearly nine years.
An interest rate increase would typically be supportive for the dollar.
UOB said that a strong non-farm payrolls report or data showing a marked improvement in the US unemployment rate “may re-ignite expectations that the Fed may start to normalise interest rates earlier rather than later and send the dollar soaring again”.
The dollar also firmed up against other Asian currencies.
It rose to 1,079.60 South Korean won from 1,078.54 on Friday, to Tw$30.68 from Tw$30.64, to 33.27 Thai baht from 33.03 and to 13,011 Indonesian rupiah from 12,970.
The dollar also advanced to 44.63 Philippine pesos from 44.59, to 63.4225 Indian rupees from 63.4200 and to Sg$1.3319 from Sg$1.3237.
The Australian dollar fell to 78.24 US cents from 78.90 US cents, while the Chinese yuan climbed to 19.3415 Japanese yen from 19.28 yen. (AFP)