Vietcombank sold the currency at VND26,335, up 0.06% from the weekend. On the black market, the greenback fell 0.04% to VND26,450.
The State Bank of Vietnam hiked its reference rate by 0.07% to VND25,182.
Globally, the euro rose against the greenback on Monday after the U.S. and the European Union announced a framework trade agreement, one of several recent deals aimed at easing global trade tensions, according to Reuters.
The euro rose 0.2% to $1.1763 and similarly strengthened against the yen to 173.78.
The dollar index, which measures the greenback against a basket of major currencies, slipped 0.1% to 97.534. The dollar held steady at 147.68 yen.
Sterling was slightly lower at $1.34385, down almost 0.1%. The Australian dollar strengthened 0.2% to $0.6576, while New Zealand's kiwi dollar was flat at $0.6019.