The Fed's emergency move, precipitated by a global equities market rout, has wiped out the dollar's yield advantage over the euro. The Fed funds rate target is now at 3.5 percent.
The euro traded up 0.8 percent from late Monday at $1.4563 after briefly racing to $1.4592 shortly after the Fed's unscheduled announcement. Against the Swiss franc, the dollar was down 0.8 percent to 1.0993 francs.
Against the yen, the dollar was up 0.3 percent at 106.30 yen, helped by a slight boost in sentiment for U.S. equities.
The Fed's move helped U.S. stock index futures to cut losses, but some analysts said the step was a sign of panic on the part on monetary authorities.