The euro lost 0.15 percent compared to the dollar to go for 1.20602. It's daily low against the greenback was 1.20564. Over the past month, the euro fell 1.52 percent compared to the dollar.
Germany's benchmark DAX index turned to gains following a lower open earlier on Monday.
With no significant data releases, traders focused on the coronavirus pandemic as well as Armin Laschet being elected the new chairman of the Christian Democratic Union (CDU). Markets in the United States were closed for Martin Luther King Jr. Day.
The DAX was up 0.25 percent as Infineon and Adidas led the gains in Frankfurt. At the same time, the FTSE 100 and the CAC 40 were flat, also following lower opens.