The Dollar Index was last at 89.704, not far from its recent 2-1/2-year low of 89.515 having shed almost 7% in 2020.
The euro pushed back up to $1.2252, having run into profit-taking late last week when it reached the highest since early 2018 at $1.2309. It gained almost 9% over 2020.
The dollar slipped to 103.02 yen, and looked in danger of testing key support at 102.55. Sterling formed at $1.3690, levels last seen in mid-2018.
In the cryptocurrency space, Bitcoin steadied at $33,102, after touching an historic top at $34,800.
The decline in the dollar has been a support for gold, leaving the metal 1.3% firmer at $1,922 an ounce.
Oil prices extended their rise after a couple of months of solid gains, with Brent testing resistance around $52.50 a barrel.
The pan-European Stoxx 50 climbed down by 0.27% to 3,571.. In the cash markets, the DAX futures Germany was trading 0.31% lower at 13,718.38. CAC 40 futures in France climbed down by 0.86% to 5,511.41, while the FTSE 100 futures in the U.K. fell by 1.45% to 6460.52,at the time of writing.