The currency is down by 0.2% at 1.0613 against the dollar as of 8:02 a.m. ET.
Monday was the first day since the US election that the euro did not finish in the red.
"The euro's downtrend does not appear over," argued Marc Chandler, the global head of currency strategy, in commentary.
"One of the key drivers pushing the euro lower is the widening interest rate differentials in the dollar's favor. The premium the US charges is still rising."
As for the rest of the world, here's the scoreboard as of 7:52 a.m. ET:
- The British pound is down by 0.4% at 1.2441 against the dollar.
- The Japanese yen is down by 0.2% at 110.98 per dollar.
- The US dollar index is little changed at 100.97.
- The Russian ruble is little changed at 63.9235 per dollar, while Brent crude oil, the international benchmark, is also little changed at $48.84 per barrel.