Vietcombank sold the dollar at VND25,464, down 0.04% from the weekend.
The greenback is steady at VND25,980 on the black market.
The State Bank of Vietnam (SBV) lowered its reference rate by 0.03% to VND24,252.
The dollar has increased against the dong by 4.28% since the beginning of the year.
Globally, the euro rose on Monday after the first round of France's snap election put the far-right in pole position, though by a smaller margin than projected, while a downgrade to Japan's first-quarter growth figures knocked the yen lower, Reuters reported.
The euro, which has fallen some 0.8% since President Emmanuel Macron called the election on June 9, was last 0.24% higher at $1.0737, after having touched a more than one-week top of $1.0749 earlier in the session.
The rise in the euro sent the dollar a touch lower against a basket of currencies , though the greenback was also reeling from data on Friday that showed U.S. inflation cooled in May, cementing expectations the Federal Reserve will begin cutting interest rates later this year.
The yen struggled to gain ground against a broadly weaker dollar, and was last 0.05% lower at 160.93 per dollar.
The dollar index was down 0.1% at 105.6.