"The first week in office was really not focused on fiscal policy or growth or any of the supply-side enhancing measures," said Mark McCormick, North American head of FX strategy at TD Securities in Toronto.
"It was really focused on all the negatives around immigration, trade risks, some of the other negative issues, which the market hasn't really been focused on."
The dollar remained weak against the yen, falling by 1.18 percent to 113.70 yen, as investors sought the traditional security of the Japanese currency as the immigration curbs put the spotlight back on Trump's protectionist bent and the risks it poses for the economy.
"The dollar is being sold a bit because of the reaction to Trump's executive order on immigration, just thinking it could create all sorts of problems with trade partners," said Joseph Trevisani, chief market strategist at Worldwide Markets in Woodcliff Lake, New Jersey. "It's really an emotional reaction to that."
The euro fell to its lowest level since Jan. 19 against the greenback after the release of German inflation data that came in slightly weaker than expected, but retraced much of the move after investors unpacked the data, which showed German consumer price inflation hit the highest in three-and-a-half years.
The euro was last down 0.05 percent against the dollar at $1.0689.
Sterling fell 0.57 percent, helping keep the dollar index from significant losses. The index tracks the greenback against the euro, pound, yen and three other major world currencies. It was last down 0.04 percent at 100.49.
A stronger dollar was one of 2017's big calls for many investment banks and asset managers at the end of last year, but that view has been undermined by worries about how U.S. trade and diplomacy will pan out under Trump's presidency.